diff --git a/src/reader/spirv/function.cc b/src/reader/spirv/function.cc
index 94aa686..8b2617c 100644
--- a/src/reader/spirv/function.cc
+++ b/src/reader/spirv/function.cc
@@ -23,10 +23,12 @@
 #include "source/opt/function.h"
 #include "source/opt/instruction.h"
 #include "source/opt/module.h"
+#include "src/ast/array_accessor_expression.h"
 #include "src/ast/as_expression.h"
 #include "src/ast/assignment_statement.h"
 #include "src/ast/binary_expression.h"
 #include "src/ast/identifier_expression.h"
+#include "src/ast/member_accessor_expression.h"
 #include "src/ast/scalar_constructor_expression.h"
 #include "src/ast/storage_class.h"
 #include "src/ast/uint_literal.h"
@@ -1492,32 +1494,31 @@
   return Fail() << "unhandled instruction with opcode " << inst.opcode();
 }
 
+TypedExpression FunctionEmitter::MakeOperand(
+    const spvtools::opt::Instruction& inst,
+    uint32_t operand_index) {
+  auto expr = this->MakeExpression(inst.GetSingleWordInOperand(operand_index));
+  return parser_impl_.RectifyOperandSignedness(inst.opcode(), std::move(expr));
+}
+
 TypedExpression FunctionEmitter::MaybeEmitCombinatorialValue(
     const spvtools::opt::Instruction& inst) {
   if (inst.result_id() == 0) {
     return {};
   }
 
-  // TODO(dneto): Fill in the following cases.
-
-  auto operand = [this, &inst](uint32_t operand_index) {
-    auto expr =
-        this->MakeExpression(inst.GetSingleWordInOperand(operand_index));
-    return parser_impl_.RectifyOperandSignedness(inst.opcode(),
-                                                 std::move(expr));
-  };
+  const auto opcode = inst.opcode();
 
   ast::type::Type* ast_type =
       inst.type_id() != 0 ? parser_impl_.ConvertType(inst.type_id()) : nullptr;
 
-  auto binary_op = ConvertBinaryOp(inst.opcode());
+  auto binary_op = ConvertBinaryOp(opcode);
   if (binary_op != ast::BinaryOp::kNone) {
-    auto arg0 = operand(0);
-    auto arg1 = operand(1);
+    auto arg0 = MakeOperand(inst, 0);
+    auto arg1 = MakeOperand(inst, 1);
     auto binary_expr = std::make_unique<ast::BinaryExpression>(
         binary_op, std::move(arg0.expr), std::move(arg1.expr));
-    auto* forced_result_ty =
-        parser_impl_.ForcedResultType(inst.opcode(), arg0.type);
+    auto* forced_result_ty = parser_impl_.ForcedResultType(opcode, arg0.type);
     if (forced_result_ty && forced_result_ty != ast_type) {
       return {ast_type, std::make_unique<ast::AsExpression>(
                             ast_type, std::move(binary_expr))};
@@ -1526,12 +1527,11 @@
   }
 
   auto unary_op = ast::UnaryOp::kNegation;
-  if (GetUnaryOp(inst.opcode(), &unary_op)) {
-    auto arg0 = operand(0);
+  if (GetUnaryOp(opcode, &unary_op)) {
+    auto arg0 = MakeOperand(inst, 0);
     auto unary_expr = std::make_unique<ast::UnaryOpExpression>(
         unary_op, std::move(arg0.expr));
-    auto* forced_result_ty =
-        parser_impl_.ForcedResultType(inst.opcode(), arg0.type);
+    auto* forced_result_ty = parser_impl_.ForcedResultType(opcode, arg0.type);
     if (forced_result_ty && forced_result_ty != ast_type) {
       return {ast_type, std::make_unique<ast::AsExpression>(
                             ast_type, std::move(unary_expr))};
@@ -1539,16 +1539,19 @@
     return {ast_type, std::move(unary_expr)};
   }
 
-  if (inst.opcode() == SpvOpBitcast) {
-    auto* target_ty = parser_impl_.ConvertType(inst.type_id());
-    return {target_ty,
-            std::make_unique<ast::AsExpression>(target_ty, operand(0).expr)};
+  if (opcode == SpvOpAccessChain || opcode == SpvOpInBoundsAccessChain) {
+    return MakeAccessChain(inst);
   }
 
-  auto negated_op = NegatedFloatCompare(inst.opcode());
+  if (opcode == SpvOpBitcast) {
+    return {ast_type, std::make_unique<ast::AsExpression>(
+                          ast_type, MakeOperand(inst, 0).expr)};
+  }
+
+  auto negated_op = NegatedFloatCompare(opcode);
   if (negated_op != ast::BinaryOp::kNone) {
-    auto arg0 = operand(0);
-    auto arg1 = operand(1);
+    auto arg0 = MakeOperand(inst, 0);
+    auto arg1 = MakeOperand(inst, 1);
     auto binary_expr = std::make_unique<ast::BinaryExpression>(
         negated_op, std::move(arg0.expr), std::move(arg1.expr));
     auto negated_expr = std::make_unique<ast::UnaryOpExpression>(
@@ -1578,8 +1581,6 @@
   //    OpGenericCastToPtr // Not in Vulkan
   //    OpGenericCastToPtrExplicit // Not in Vulkan
   //
-  //    OpAccessChain
-  //    OpInBoundsAccessChain
   //    OpArrayLength
   //    OpVectorExtractDynamic
   //    OpVectorInsertDynamic
@@ -1589,6 +1590,130 @@
   return {};
 }
 
+TypedExpression FunctionEmitter::MakeAccessChain(
+    const spvtools::opt::Instruction& inst) {
+  if (inst.NumInOperands() < 1) {
+    // Binary parsing will fail on this anyway.
+    Fail() << "invalid access chain: has no input operands";
+    return {};
+  }
+
+  // A SPIR-V access chain is a single instruction with multiple indices
+  // walking down into composites.  The Tint AST represents this as ever-deeper
+  // nested indexing expresions.
+  // Start off with an expression for the base, and then bury that inside
+  // nested indexing expressions.
+  TypedExpression current_expr(MakeOperand(inst, 0));
+
+  const auto constants = constant_mgr_->GetOperandConstants(&inst);
+  static const char* swizzles[] = {"x", "y", "z", "w"};
+
+  const auto base_id = inst.GetSingleWordInOperand(0);
+  const auto ptr_ty_id = def_use_mgr_->GetDef(base_id)->type_id();
+  const auto* ptr_type = type_mgr_->GetType(ptr_ty_id);
+  if (!ptr_type || !ptr_type->AsPointer()) {
+    Fail() << "Access chain %" << inst.result_id()
+                  << " base pointer is not of pointer type";
+    return {};
+  }
+  const auto* pointee_type = ptr_type->AsPointer()->pointee_type();
+  const auto num_in_operands = inst.NumInOperands();
+  for (uint32_t index = 1; index < num_in_operands; ++index) {
+    const auto* index_const =
+        constants[index] ? constants[index]->AsIntConstant() : nullptr;
+    const int64_t index_const_val =
+        index_const ? index_const->GetSignExtendedValue() : 0;
+    std::unique_ptr<ast::Expression> next_expr;
+    switch (pointee_type->kind()) {
+      case spvtools::opt::analysis::Type::kVector:
+        if (index_const) {
+          // Try generating a MemberAccessor expression.
+          if (index_const_val < 0 ||
+              pointee_type->AsVector()->element_count() <= index_const_val) {
+            Fail() << "Access chain %" << inst.result_id() << " index %"
+                          << inst.GetSingleWordInOperand(index) << " value "
+                          << index_const_val
+                          << " is out of bounds for vector of "
+                          << pointee_type->AsVector()->element_count()
+                          << " elements";
+            return {};
+          }
+          if (uint64_t(index_const_val) >=
+              sizeof(swizzles) / sizeof(swizzles[0])) {
+            Fail() << "internal error: swizzle index " << index_const_val
+                   << " is too big. Max handled index is "
+                   << ((sizeof(swizzles) / sizeof(swizzles[0])) - 1);
+          }
+          auto letter_index = std::make_unique<ast::IdentifierExpression>(
+              swizzles[index_const_val]);
+          next_expr = std::make_unique<ast::MemberAccessorExpression>(
+              std::move(current_expr.expr), std::move(letter_index));
+        } else {
+          // Non-constant index. Use array syntax
+          next_expr = std::make_unique<ast::ArrayAccessorExpression>(
+              std::move(current_expr.expr),
+              std::move(MakeOperand(inst, index).expr));
+        }
+        pointee_type = pointee_type->AsVector()->element_type();
+        break;
+      case spvtools::opt::analysis::Type::kMatrix:
+        // Use array syntax.
+        next_expr = std::make_unique<ast::ArrayAccessorExpression>(
+            std::move(current_expr.expr), std::move(MakeOperand(inst, index).expr));
+        pointee_type = pointee_type->AsMatrix()->element_type();
+        break;
+      case spvtools::opt::analysis::Type::kArray:
+        next_expr = std::make_unique<ast::ArrayAccessorExpression>(
+            std::move(current_expr.expr), std::move(MakeOperand(inst, index).expr));
+        pointee_type = pointee_type->AsArray()->element_type();
+        break;
+      case spvtools::opt::analysis::Type::kRuntimeArray:
+        next_expr = std::make_unique<ast::ArrayAccessorExpression>(
+            std::move(current_expr.expr), std::move(MakeOperand(inst, index).expr));
+        pointee_type = pointee_type->AsRuntimeArray()->element_type();
+        break;
+      case spvtools::opt::analysis::Type::kStruct: {
+        if (!index_const) {
+          Fail() << "Access chain %" << inst.result_id() << " index %"
+                        << inst.GetSingleWordInOperand(index)
+                        << " is a non-constant index into a structure %"
+                        << type_mgr_->GetId(pointee_type);
+          return {};
+        }
+        if ((index_const_val < 0) ||
+            pointee_type->AsStruct()->element_types().size() <=
+                uint64_t(index_const_val)) {
+          Fail() << "Access chain %" << inst.result_id()
+                        << " index value " << index_const_val
+                        << " is out of bounds for structure %"
+                        << type_mgr_->GetId(pointee_type) << " having "
+                        << pointee_type->AsStruct()->element_types().size()
+                        << " elements";
+          return {};
+        }
+        auto member_access =
+            std::make_unique<ast::IdentifierExpression>(namer_.GetMemberName(
+                type_mgr_->GetId(pointee_type), uint32_t(index_const_val)));
+
+        next_expr = std::make_unique<ast::MemberAccessorExpression>(
+            std::move(current_expr.expr), std::move(member_access));
+        pointee_type =
+            pointee_type->AsStruct()->element_types()[index_const_val];
+        break;
+     }
+      default:
+        Fail() << "Access chain with unknown pointee type %"
+                      << type_mgr_->GetId(pointee_type) << " "
+                      << pointee_type->str();
+        return {};
+    }
+    current_expr.reset(TypedExpression(
+          parser_impl_.ConvertType(type_mgr_->GetId(pointee_type)),
+          std::move(next_expr)));
+  }
+  return current_expr;
+}
+
 }  // namespace spirv
 }  // namespace reader
 }  // namespace tint
diff --git a/src/reader/spirv/function.h b/src/reader/spirv/function.h
index 86a9a6f..36490d4 100644
--- a/src/reader/spirv/function.h
+++ b/src/reader/spirv/function.h
@@ -316,6 +316,21 @@
   ast::type::Type* GetVariableStoreType(
       const spvtools::opt::Instruction& var_decl_inst);
 
+  /// Returns an expression for an instruction operand. Signedness conversion is
+  /// performed to match the result type of the SPIR-V instruction.
+  /// @param inst the SPIR-V instruction
+  /// @param operand_index the index of the operand, counting 0 as the first
+  /// input operand
+  /// @returns a new expression node
+  TypedExpression MakeOperand(const spvtools::opt::Instruction& inst,
+                              uint32_t operand_index);
+
+  /// Returns an expression for a SPIR-V OpAccessChain or OpInBoundsAccessChain
+  /// instruction.
+  /// @param inst the SPIR-V instruction
+  /// @returns an expression
+  TypedExpression MakeAccessChain(const spvtools::opt::Instruction& inst);
+
   /// Finds the header block for a structured construct that we can "break"
   /// out from, from deeply nested control flow, if such a block exists.
   /// If the construct is:
diff --git a/src/reader/spirv/function_memory_test.cc b/src/reader/spirv/function_memory_test.cc
index aafc6cb..5bdfb2c 100644
--- a/src/reader/spirv/function_memory_test.cc
+++ b/src/reader/spirv/function_memory_test.cc
@@ -26,6 +26,7 @@
 namespace spirv {
 namespace {
 
+using ::testing::Eq;
 using ::testing::HasSubstr;
 
 TEST_F(SpvParserTest, EmitStatement_StoreBoolConst) {
@@ -279,6 +280,434 @@
 })"));
 }
 
+TEST_F(SpvParserTest, EmitStatement_AccessChain_NoOperands) {
+  auto err = test::AssembleFailure(R"(
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %ty = OpTypeInt 32 0
+     %val = OpConstant %ty 42
+     %ptr_ty = OpTypePointer Workgroup %ty
+     %1 = OpVariable %ptr_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+
+     %2 = OpAccessChain %ptr_ty  ; Needs a base operand
+     OpStore %1 %val
+     OpReturn
+  )");
+  EXPECT_THAT(err,
+              Eq("11:5: Expected operand, found next instruction instead."));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_BaseIsNotPointer) {
+  auto* p = parser(test::Assemble(R"(
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %10 = OpTypeInt 32 0
+     %val = OpConstant %10 42
+     %ptr_ty = OpTypePointer Workgroup %10
+     %20 = OpVariable %10 Workgroup ; bad pointer type
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %1 = OpAccessChain %ptr_ty %20
+     OpStore %1 %val
+     OpReturn
+  )"));
+  EXPECT_FALSE(p->BuildAndParseInternalModuleExceptFunctions());
+  EXPECT_THAT(p->error(), Eq("variable with ID 20 has non-pointer type 10"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_VectorSwizzle) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %uint = OpTypeInt 32 0
+     %store_ty = OpTypeVector %uint 4
+     %uint_2 = OpConstant %uint 2
+     %uint_42 = OpConstant %uint 42
+     %elem_ty = OpTypePointer Workgroup %uint
+     %var_ty = OpTypePointer Workgroup %store_ty
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_2
+     OpStore %2 %uint_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  MemberAccessor{
+    Identifier{myvar}
+    Identifier{z}
+  }
+  ScalarConstructor{42}
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_VectorConstOutOfBounds) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %uint = OpTypeInt 32 0
+     %store_ty = OpTypeVector %uint 4
+     %42 = OpConstant %uint 42
+     %uint_99 = OpConstant %uint 99
+     %elem_ty = OpTypePointer Workgroup %uint
+     %var_ty = OpTypePointer Workgroup %store_ty
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %42
+     OpStore %2 %uint_99
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_FALSE(fe.EmitBody());
+  EXPECT_THAT(p->error(), Eq("Access chain %2 index %42 value 42 is out of "
+                             "bounds for vector of 4 elements"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_VectorNonConstIndex) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %uint = OpTypeInt 32 0
+     %store_ty = OpTypeVector %uint 4
+     %uint_2 = OpConstant %uint 2
+     %uint_42 = OpConstant %uint 42
+     %elem_ty = OpTypePointer Workgroup %uint
+     %var_ty = OpTypePointer Workgroup %store_ty
+     %1 = OpVariable %var_ty Workgroup
+     %10 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %11 = OpLoad %uint %10
+     %2 = OpAccessChain %elem_ty %1 %11
+     OpStore %2 %uint_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  ArrayAccessor{
+    Identifier{myvar}
+    Identifier{x_11}
+  }
+  ScalarConstructor{42}
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_Matrix) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %v4float = OpTypeVector %float 4
+     %m3v4float = OpTypeMatrix %v4float 3
+     %elem_ty = OpTypePointer Workgroup %v4float
+     %var_ty = OpTypePointer Workgroup %m3v4float
+     %uint = OpTypeInt 32 0
+     %uint_2 = OpConstant %uint 2
+     %float_42 = OpConstant %float 42
+     %v4float_42 = OpConstantComposite %v4float %float_42 %float_42 %float_42 %float_42
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_2
+     OpStore %2 %v4float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  ArrayAccessor{
+    Identifier{myvar}
+    ScalarConstructor{2}
+  }
+  TypeConstructor{
+    __vec_4__f32
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+  }
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_Array) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %v4float = OpTypeVector %float 4
+     %m3v4float = OpTypeMatrix %v4float 3
+     %elem_ty = OpTypePointer Workgroup %v4float
+     %var_ty = OpTypePointer Workgroup %m3v4float
+     %uint = OpTypeInt 32 0
+     %uint_2 = OpConstant %uint 2
+     %float_42 = OpConstant %float 42
+     %v4float_42 = OpConstantComposite %v4float %float_42 %float_42 %float_42 %float_42
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_2
+     OpStore %2 %v4float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  ArrayAccessor{
+    Identifier{myvar}
+    ScalarConstructor{2}
+  }
+  TypeConstructor{
+    __vec_4__f32
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+    ScalarConstructor{42.000000}
+  }
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_Struct) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     OpMemberName %strct 1 "age"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %float_42 = OpConstant %float 42
+     %strct = OpTypeStruct %float %float
+     %elem_ty = OpTypePointer Workgroup %float
+     %var_ty = OpTypePointer Workgroup %strct
+     %uint = OpTypeInt 32 0
+     %uint_1 = OpConstant %uint 1
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_1
+     OpStore %2 %float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  MemberAccessor{
+    Identifier{myvar}
+    Identifier{age}
+  }
+  ScalarConstructor{42.000000}
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_StructNonConstIndex) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     OpMemberName %55 1 "age"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %float_42 = OpConstant %float 42
+     %55 = OpTypeStruct %float %float
+     %elem_ty = OpTypePointer Workgroup %float
+     %var_ty = OpTypePointer Workgroup %55
+     %uint = OpTypeInt 32 0
+     %uint_1 = OpConstant %uint 1
+     %uint_ptr = OpTypePointer Workgroup %uint
+     %uintvar = OpVariable %uint_ptr Workgroup
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %10 = OpLoad %uint %uintvar
+     %2 = OpAccessChain %elem_ty %1 %10
+     OpStore %2 %float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_FALSE(fe.EmitBody());
+  EXPECT_THAT(p->error(), Eq("Access chain %2 index %10 is a non-constant "
+                             "index into a structure %55"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_StructConstOutOfBounds) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     OpMemberName %55 1 "age"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %float_42 = OpConstant %float 42
+     %55 = OpTypeStruct %float %float
+     %elem_ty = OpTypePointer Workgroup %float
+     %var_ty = OpTypePointer Workgroup %55
+     %uint = OpTypeInt 32 0
+     %uint_99 = OpConstant %uint 99
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_99
+     OpStore %2 %float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_FALSE(fe.EmitBody());
+  EXPECT_THAT(p->error(), Eq("Access chain %2 index value 99 is out of bounds "
+                             "for structure %55 having 2 elements"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_Struct_RuntimeArray) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     OpMemberName %strct 1 "age"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %float_42 = OpConstant %float 42
+     %rtarr = OpTypeRuntimeArray %float
+     %strct = OpTypeStruct %float %rtarr
+     %elem_ty = OpTypePointer Workgroup %float
+     %var_ty = OpTypePointer Workgroup %strct
+     %uint = OpTypeInt 32 0
+     %uint_1 = OpConstant %uint 1
+     %uint_2 = OpConstant %uint 2
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_1 %uint_2
+     OpStore %2 %float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  ArrayAccessor{
+    MemberAccessor{
+      Identifier{myvar}
+      Identifier{age}
+    }
+    ScalarConstructor{2}
+  }
+  ScalarConstructor{42.000000}
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_Compound_Matrix_Vector) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %void = OpTypeVoid
+     %voidfn = OpTypeFunction %void
+     %float = OpTypeFloat 32
+     %v4float = OpTypeVector %float 4
+     %m3v4float = OpTypeMatrix %v4float 3
+     %elem_ty = OpTypePointer Workgroup %float
+     %var_ty = OpTypePointer Workgroup %m3v4float
+     %uint = OpTypeInt 32 0
+     %uint_2 = OpConstant %uint 2
+     %uint_3 = OpConstant %uint 3
+     %float_42 = OpConstant %float 42
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %void None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %elem_ty %1 %uint_2 %uint_3
+     OpStore %2 %float_42
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_TRUE(fe.EmitBody());
+  EXPECT_THAT(ToString(fe.ast_body()), HasSubstr(R"(Assignment{
+  MemberAccessor{
+    ArrayAccessor{
+      Identifier{myvar}
+      ScalarConstructor{2}
+    }
+    Identifier{w}
+  }
+  ScalarConstructor{42.000000}
+})"));
+}
+
+TEST_F(SpvParserTest, EmitStatement_AccessChain_InvalidPointeeType) {
+  const std::string assembly = R"(
+     OpName %1 "myvar"
+     %55 = OpTypeVoid
+     %voidfn = OpTypeFunction %55
+     %float = OpTypeFloat 32
+     %60 = OpTypePointer Workgroup %55
+     %var_ty = OpTypePointer Workgroup %60
+     %uint = OpTypeInt 32 0
+     %uint_2 = OpConstant %uint 2
+
+     %1 = OpVariable %var_ty Workgroup
+     %100 = OpFunction %55 None %voidfn
+     %entry = OpLabel
+     %2 = OpAccessChain %60 %1 %uint_2
+     OpReturn
+     OpFunctionEnd
+  )";
+  auto* p = parser(test::Assemble(assembly));
+  ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions())
+      << assembly << p->error();
+  FunctionEmitter fe(p, *spirv_function(100));
+  EXPECT_FALSE(fe.EmitBody());
+  EXPECT_THAT(p->error(),
+              HasSubstr("Access chain with unknown pointee type %60 void"));
+}
+
 }  // namespace
 }  // namespace spirv
 }  // namespace reader
diff --git a/src/reader/spirv/parser_impl.cc b/src/reader/spirv/parser_impl.cc
index a09401c..29a952e 100644
--- a/src/reader/spirv/parser_impl.cc
+++ b/src/reader/spirv/parser_impl.cc
@@ -183,6 +183,11 @@
 
 TypedExpression::~TypedExpression() {}
 
+void TypedExpression::reset(TypedExpression&& other) {
+  type = other.type;
+  expr = std::move(other.expr);
+}
+
 ParserImpl::ParserImpl(Context* ctx, const std::vector<uint32_t>& spv_binary)
     : Reader(ctx),
       spv_binary_(spv_binary),
@@ -786,6 +791,10 @@
                        "SPIR-V type with ID: "
                     << var.type_id();
     }
+    if (!ast_type->IsPointer()) {
+      return Fail() << "variable with ID " << var.result_id()
+                    << " has non-pointer type " << var.type_id();
+    }
     auto* ast_store_type = ast_type->AsPointer()->type();
     auto ast_var =
         MakeVariable(var.result_id(), ast_storage_class, ast_store_type);
diff --git a/src/reader/spirv/parser_impl.h b/src/reader/spirv/parser_impl.h
index 554fe27..d99b73c 100644
--- a/src/reader/spirv/parser_impl.h
+++ b/src/reader/spirv/parser_impl.h
@@ -65,6 +65,9 @@
   TypedExpression(TypedExpression&& other);
   /// Destructor
   ~TypedExpression();
+  /// Takes values from another typed expression.
+  /// @param other the other typed expression
+  void reset(TypedExpression&& other);
   /// The type
   ast::type::Type* type;
   /// The expression
diff --git a/src/reader/spirv/parser_impl_module_var_test.cc b/src/reader/spirv/parser_impl_module_var_test.cc
index d46ab0a..ef06c26 100644
--- a/src/reader/spirv/parser_impl_module_var_test.cc
+++ b/src/reader/spirv/parser_impl_module_var_test.cc
@@ -99,6 +99,20 @@
                                     "AST type for SPIR-V type with ID: 3"));
 }
 
+TEST_F(SpvParserTest, ModuleScopeVar_NonPointerType) {
+  auto* p = parser(test::Assemble(R"(
+    %float = OpTypeFloat 32
+    %5 = OpTypeFunction %float
+    %3 = OpTypePointer Private %5
+    %52 = OpVariable %float Private
+  )"));
+  EXPECT_TRUE(p->BuildInternalModule());
+  EXPECT_FALSE(p->RegisterTypes());
+  EXPECT_THAT(
+      p->error(),
+      HasSubstr("SPIR-V pointer type with ID 3 has invalid pointee type 5"));
+}
+
 TEST_F(SpvParserTest, ModuleScopeVar_AnonWorkgroupVar) {
   auto* p = parser(test::Assemble(R"(
     %float = OpTypeFloat 32
diff --git a/src/reader/spirv/spirv_tools_helpers_test.cc b/src/reader/spirv/spirv_tools_helpers_test.cc
index 2a31f7d..81dd5e7 100644
--- a/src/reader/spirv/spirv_tools_helpers_test.cc
+++ b/src/reader/spirv/spirv_tools_helpers_test.cc
@@ -49,6 +49,26 @@
   return result;
 }
 
+std::string AssembleFailure(const std::string& spirv_assembly) {
+  // TODO(dneto): Use ScopedTrace?
+
+  // (The target environment doesn't affect assembly.
+  spvtools::SpirvTools tools(SPV_ENV_UNIVERSAL_1_0);
+  std::stringstream errors;
+  std::vector<uint32_t> result;
+  tools.SetMessageConsumer([&errors](spv_message_level_t, const char*,
+                                     const spv_position_t& position,
+                                     const char* message) {
+    errors << position.line << ":" << position.column << ": " << message;
+  });
+
+  const auto success = tools.Assemble(
+      spirv_assembly, &result, SPV_TEXT_TO_BINARY_OPTION_PRESERVE_NUMERIC_IDS);
+  EXPECT_FALSE(success);
+
+  return errors.str();
+}
+
 }  // namespace test
 }  // namespace spirv
 }  // namespace reader
diff --git a/src/reader/spirv/spirv_tools_helpers_test.h b/src/reader/spirv/spirv_tools_helpers_test.h
index d6db2a1..ba4ad68 100644
--- a/src/reader/spirv/spirv_tools_helpers_test.h
+++ b/src/reader/spirv/spirv_tools_helpers_test.h
@@ -28,6 +28,10 @@
 /// are preserved.
 std::vector<uint32_t> Assemble(const std::string& spirv_assembly);
 
+/// Attempts to assemble given SPIR-V assembly text.  Expect it to fail.
+/// @returns the failure message.
+std::string AssembleFailure(const std::string& spirv_assembly);
+
 }  // namespace test
 }  // namespace spirv
 }  // namespace reader