diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 7b96830da9..1c0d736982 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -325,6 +325,7 @@ if(${TINT_BUILD_SPV_READER})
     reader/spirv/parser_impl_convert_member_decoration_test.cc
     reader/spirv/parser_impl_convert_type_test.cc
     reader/spirv/parser_impl_entry_point_test.cc
+    reader/spirv/parser_impl_function_decl_test.cc
     reader/spirv/parser_impl_get_decorations_test.cc
     reader/spirv/parser_impl_import_test.cc
     reader/spirv/parser_impl_module_var_test.cc
diff --git a/src/reader/spirv/parser_impl.cc b/src/reader/spirv/parser_impl.cc
index e843e72299..e1641c69a4 100644
--- a/src/reader/spirv/parser_impl.cc
+++ b/src/reader/spirv/parser_impl.cc
@@ -19,10 +19,14 @@
 #include <limits>
 #include <memory>
 #include <string>
+#include <unordered_map>
+#include <unordered_set>
 #include <utility>
 
+#include "source/opt/basic_block.h"
 #include "source/opt/build_module.h"
 #include "source/opt/decoration_manager.h"
+#include "source/opt/function.h"
 #include "source/opt/instruction.h"
 #include "source/opt/module.h"
 #include "source/opt/type_manager.h"
@@ -60,6 +64,53 @@ namespace {
 
 const spv_target_env kTargetEnv = SPV_ENV_WEBGPU_0;
 
+// A FunctionTraverser is used to compute an ordering of functions in the
+// module such that callees precede callers.
+class FunctionTraverser {
+ public:
+  explicit FunctionTraverser(const spvtools::opt::Module& module)
+      : module_(module) {}
+
+  // @returns the functions in the modules such that callees precede callers.
+  std::vector<const spvtools::opt::Function*> TopologicallyOrderedFunctions() {
+    visited_.clear();
+    ordered_.clear();
+    id_to_func_.clear();
+    for (const auto& f : module_) {
+      id_to_func_[f.result_id()] = &f;
+    }
+    for (const auto& f : module_) {
+      Visit(f);
+    }
+    return ordered_;
+  }
+
+ private:
+  void Visit(const spvtools::opt::Function& f) {
+    if (visited_.count(&f)) {
+      return;
+    }
+    visited_.insert(&f);
+    for (const auto& bb : f) {
+      for (const auto& inst : bb) {
+        if (inst.opcode() != SpvOpFunctionCall) {
+          continue;
+        }
+        const auto* callee = id_to_func_[inst.GetSingleWordInOperand(0)];
+        if (callee) {
+          Visit(*callee);
+        }
+      }
+    }
+    ordered_.push_back(&f);
+  }
+
+  const spvtools::opt::Module& module_;
+  std::unordered_set<const spvtools::opt::Function*> visited_;
+  std::unordered_map<uint32_t, const spvtools::opt::Function*> id_to_func_;
+  std::vector<const spvtools::opt::Function*> ordered_;
+};
+
 }  // namespace
 
 ParserImpl::ParserImpl(Context* ctx, const std::vector<uint32_t>& spv_binary)
@@ -174,7 +225,10 @@ ast::type::Type* ParserImpl::ConvertType(uint32_t type_id) {
     case spvtools::opt::analysis::Type::kPointer:
       return save(ConvertType(spirv_type->AsPointer()));
     case spvtools::opt::analysis::Type::kFunction:
-      // TODO(dneto). For now return null without erroring out.
+      // Tint doesn't have a Function type.
+      // We need to convert the result type and parameter types.
+      // But the SPIR-V defines those before defining the function
+      // type.  No further work is required here.
       return nullptr;
     default:
       break;
@@ -299,8 +353,10 @@ bool ParserImpl::ParseInternalModule() {
   if (!EmitModuleScopeVariables()) {
     return false;
   }
-  // TODO(dneto): fill in the rest
-  return true;
+  if (!EmitFunctions()) {
+    return false;
+  }
+  return success_;
 }
 
 bool ParserImpl::RegisterExtendedInstructionImports() {
@@ -635,39 +691,8 @@ bool ParserImpl::EmitModuleScopeVariables() {
                     << var.type_id();
     }
     auto* ast_store_type = ast_type->AsPointer()->type();
-    if (!namer_.HasName(var.result_id())) {
-      namer_.SuggestSanitizedName(var.result_id(),
-                                  "x_" + std::to_string(var.result_id()));
-    }
-    auto ast_var = std::make_unique<ast::Variable>(
-        namer_.GetName(var.result_id()), ast_storage_class, ast_store_type);
-
-    std::vector<std::unique_ptr<ast::VariableDecoration>> ast_decorations;
-    for (auto& deco : GetDecorationsFor(var.result_id())) {
-      if (deco.empty()) {
-        return Fail() << "malformed decoration on ID " << var.result_id()
-                      << ": it is empty";
-      }
-      if (deco[0] == SpvDecorationBuiltIn) {
-        if (deco.size() == 1) {
-          return Fail() << "malformed BuiltIn decoration on ID "
-                        << var.result_id() << ": has no operand";
-        }
-        auto ast_builtin =
-            enum_converter_.ToBuiltin(static_cast<SpvBuiltIn>(deco[1]));
-        if (ast_builtin == ast::Builtin::kNone) {
-          return false;
-        }
-        ast_decorations.emplace_back(
-            std::make_unique<ast::BuiltinDecoration>(ast_builtin));
-      }
-    }
-    if (!ast_decorations.empty()) {
-      auto decorated_var =
-          std::make_unique<ast::DecoratedVariable>(std::move(ast_var));
-      decorated_var->set_decorations(std::move(ast_decorations));
-      ast_var = std::move(decorated_var);
-    }
+    auto ast_var =
+        MakeVariable(var.result_id(), ast_storage_class, ast_store_type);
 
     // TODO(dneto): initializers (a.k.a. constructor expression)
     ast_module_.AddGlobalVariable(std::move(ast_var));
@@ -675,6 +700,99 @@ bool ParserImpl::EmitModuleScopeVariables() {
   return success_;
 }
 
+std::unique_ptr<ast::Variable> ParserImpl::MakeVariable(uint32_t id,
+                                                        ast::StorageClass sc,
+                                                        ast::type::Type* type) {
+  if (type == nullptr) {
+    Fail() << "internal error: can't make ast::Variable for null type";
+    return nullptr;
+  }
+
+  auto ast_var = std::make_unique<ast::Variable>(Name(id), sc, type);
+
+  std::vector<std::unique_ptr<ast::VariableDecoration>> ast_decorations;
+  for (auto& deco : GetDecorationsFor(id)) {
+    if (deco.empty()) {
+      Fail() << "malformed decoration on ID " << id << ": it is empty";
+      return nullptr;
+    }
+    if (deco[0] == SpvDecorationBuiltIn) {
+      if (deco.size() == 1) {
+        Fail() << "malformed BuiltIn decoration on ID " << id
+               << ": has no operand";
+        return nullptr;
+      }
+      auto ast_builtin =
+          enum_converter_.ToBuiltin(static_cast<SpvBuiltIn>(deco[1]));
+      if (ast_builtin == ast::Builtin::kNone) {
+        return nullptr;
+      }
+      ast_decorations.emplace_back(
+          std::make_unique<ast::BuiltinDecoration>(ast_builtin));
+    }
+  }
+  if (!ast_decorations.empty()) {
+    auto decorated_var =
+        std::make_unique<ast::DecoratedVariable>(std::move(ast_var));
+    decorated_var->set_decorations(std::move(ast_decorations));
+    ast_var = std::move(decorated_var);
+  }
+  return ast_var;
+}
+
+bool ParserImpl::EmitFunctions() {
+  if (!success_) {
+    return false;
+  }
+  for (const auto* f :
+       FunctionTraverser(*module_).TopologicallyOrderedFunctions()) {
+    EmitFunction(*f);
+  }
+  return success_;
+}
+
+bool ParserImpl::EmitFunction(const spvtools::opt::Function& f) {
+  if (!success_) {
+    return false;
+  }
+  // We only care about functions with bodies.
+  if (f.cbegin() == f.cend()) {
+    return true;
+  }
+
+  const auto name = Name(f.result_id());
+  // Surprisingly, the "type id" on an OpFunction is the result type of the
+  // function, not the type of the function.  This is the one exceptional case
+  // in SPIR-V where the type ID is not the type of the result ID.
+  auto* ret_ty = ConvertType(f.type_id());
+  if (!success_) {
+    return false;
+  }
+  if (ret_ty == nullptr) {
+    return Fail()
+           << "internal error: unregistered return type for function with ID "
+           << f.result_id();
+  }
+
+  std::vector<std::unique_ptr<ast::Variable>> ast_params;
+  f.ForEachParam([this, &ast_params](const spvtools::opt::Instruction* param) {
+    auto* ast_type = ConvertType(param->type_id());
+    if (ast_type != nullptr) {
+      ast_params.emplace_back(std::move(MakeVariable(
+          param->result_id(), ast::StorageClass::kNone, ast_type)));
+    }
+  });
+  if (!success_) {
+    return false;
+  }
+
+  auto ast_fn =
+      std::make_unique<ast::Function>(name, std::move(ast_params), ret_ty);
+  ast_module_.AddFunction(std::move(ast_fn));
+
+  return success_;
+}
+
 }  // namespace spirv
 }  // namespace reader
 }  // namespace tint
diff --git a/src/reader/spirv/parser_impl.h b/src/reader/spirv/parser_impl.h
index 2c6a0982e8..f9a6e4553d 100644
--- a/src/reader/spirv/parser_impl.h
+++ b/src/reader/spirv/parser_impl.h
@@ -178,7 +178,26 @@ class ParserImpl : Reader {
   /// @returns true if parser is still successful.
   bool EmitModuleScopeVariables();
 
+  /// Emits functions, with callees preceding their callers.
+  /// This is a no-op if the parser has already failed.
+  /// @returns true if parser is still successful.
+  bool EmitFunctions();
+
+  /// Emits a single function, if it has a body.
+  /// This is a no-op if the parser has already failed.
+  /// @param f the function to emit
+  /// @returns true if parser is still successful.
+  bool EmitFunction(const spvtools::opt::Function& f);
+
  private:
+  /// @returns a name for the given ID. Generates a name if non exists.
+  std::string Name(uint32_t id) {
+    if (!namer_.HasName(id)) {
+      namer_.SuggestSanitizedName(id, "x_" + std::to_string(id));
+    }
+    return namer_.GetName(id);
+  }
+
   /// Converts a specific SPIR-V type to a Tint type. Integer case
   ast::type::Type* ConvertType(const spvtools::opt::analysis::Integer* int_ty);
   /// Converts a specific SPIR-V type to a Tint type. Float case
@@ -198,6 +217,16 @@ class ParserImpl : Reader {
   /// Converts a specific SPIR-V type to a Tint type. Pointer case
   ast::type::Type* ConvertType(const spvtools::opt::analysis::Pointer* ptr_ty);
 
+  /// Creates an AST Variable node for a SPIR-V ID, including any attached
+  /// decorations.
+  /// @param id the SPIR-V result ID
+  /// @param sc the storage class, which can be ast::StorageClass::kNone
+  /// @param type the type
+  /// @returns a new Variable node, or null in the error case
+  std::unique_ptr<ast::Variable> MakeVariable(uint32_t id,
+                                              ast::StorageClass sc,
+                                              ast::type::Type* type);
+
   // The SPIR-V binary we're parsing
   std::vector<uint32_t> spv_binary_;
 
diff --git a/src/reader/spirv/parser_impl_function_decl_test.cc b/src/reader/spirv/parser_impl_function_decl_test.cc
new file mode 100644
index 0000000000..e95cab8d39
--- /dev/null
+++ b/src/reader/spirv/parser_impl_function_decl_test.cc
@@ -0,0 +1,224 @@
+// Copyright 2020 The Tint Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <sstream>
+#include <string>
+#include <vector>
+
+#include "gmock/gmock.h"
+#include "src/reader/spirv/parser_impl.h"
+#include "src/reader/spirv/parser_impl_test_helper.h"
+#include "src/reader/spirv/spirv_tools_helpers_test.h"
+
+namespace tint {
+namespace reader {
+namespace spirv {
+namespace {
+
+using ::testing::HasSubstr;
+
+/// @returns a SPIR-V assembly segment which assigns debug names
+/// to particular IDs.
+std::string Names(std::vector<std::string> ids) {
+  std::ostringstream outs;
+  for (auto& id : ids) {
+    outs << "    OpName %" << id << " \"" << id << "\"\n";
+  }
+  return outs.str();
+}
+
+std::string CommonTypes() {
+  return R"(
+    %void = OpTypeVoid
+    %voidfn = OpTypeFunction %void
+    %float = OpTypeFloat 32
+    %uint = OpTypeInt 32 0
+    %int = OpTypeInt 32 1
+    %float_0 = OpConstant %float 0.0
+  )";
+}
+
+TEST_F(SpvParserTest, EmitFunctions_NoFunctions) {
+  auto p = parser(test::Assemble(CommonTypes()));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, Not(HasSubstr("Function{")));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_FunctionWithoutBody) {
+  auto p = parser(test::Assemble(Names({"main"}) + CommonTypes() + R"(
+     %main = OpFunction %void None %voidfn
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, Not(HasSubstr("Function{")));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_VoidFunctionWithoutParams) {
+  auto p = parser(test::Assemble(Names({"main"}) + CommonTypes() + R"(
+     %main = OpFunction %void None %voidfn
+     %entry = OpLabel
+     OpReturn
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, HasSubstr(R"(
+  Function main -> __void
+  ()
+  {)"));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_CalleePrecedesCaller) {
+  auto p = parser(
+      test::Assemble(Names({"root", "branch", "leaf"}) + CommonTypes() + R"(
+     %root = OpFunction %void None %voidfn
+     %root_entry = OpLabel
+     %branch_result = OpFunctionCall %void %branch
+     OpReturn
+     OpFunctionEnd
+
+     %branch = OpFunction %void None %voidfn
+     %branch_entry = OpLabel
+     %leaf_result = OpFunctionCall %void %leaf
+     OpReturn
+     OpFunctionEnd
+
+     %leaf = OpFunction %void None %voidfn
+     %leaf_entry = OpLabel
+     OpReturn
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, HasSubstr(R"(
+  Function leaf -> __void
+  ()
+  {
+  }
+  Function branch -> __void
+  ()
+  {
+  }
+  Function root -> __void
+  ()
+  {
+  })"));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_NonVoidResultType) {
+  auto p = parser(test::Assemble(Names({"ret_float"}) + CommonTypes() + R"(
+     %fn_ret_float = OpTypeFunction %float
+
+     %ret_float = OpFunction %float None %nf_ret_float
+     %ret_float_entry = OpLabel
+     OpReturnValue %float_0
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, HasSubstr(R"(
+  Function ret_float -> __f32
+  ()
+  {
+  })"));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_MixedParamTypes) {
+  auto p = parser(test::Assemble(Names({"mixed_params", "a", "b", "c"}) +
+                                 CommonTypes() + R"(
+     %fn_mixed_params = OpTypeFunction %float %uint %float %int
+
+     %mixed_params = OpFunction %void None %fn_mixed_params
+     %a = OpFunctionParameter %uint
+     %b = OpFunctionParameter %float
+     %c = OpFunctionParameter %int
+     %mixed_entry = OpLabel
+     OpReturn
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, HasSubstr(R"(
+  Function mixed_params -> __void
+  (
+    Variable{
+      a
+      none
+      __u32
+    }
+    Variable{
+      b
+      none
+      __f32
+    }
+    Variable{
+      c
+      none
+      __i32
+    }
+  )
+  {
+  })"));
+}
+
+TEST_F(SpvParserTest, EmitFunctions_GenerateParamNames) {
+  auto p = parser(test::Assemble(Names({"mixed_params"}) + CommonTypes() + R"(
+     %fn_mixed_params = OpTypeFunction %float %uint %float %int
+
+     %mixed_params = OpFunction %void None %fn_mixed_params
+     %14 = OpFunctionParameter %uint
+     %15 = OpFunctionParameter %float
+     %16 = OpFunctionParameter %int
+     %mixed_entry = OpLabel
+     OpReturn
+     OpFunctionEnd
+  )"));
+  EXPECT_TRUE(p->BuildAndParseInternalModule());
+  EXPECT_TRUE(p->error().empty());
+  const auto module_ast = p->module().to_str();
+  EXPECT_THAT(module_ast, HasSubstr(R"(
+  Function mixed_params -> __void
+  (
+    Variable{
+      x_14
+      none
+      __u32
+    }
+    Variable{
+      x_15
+      none
+      __f32
+    }
+    Variable{
+      x_16
+      none
+      __i32
+    }
+  )
+  {
+  })"));
+}
+
+}  // namespace
+}  // namespace spirv
+}  // namespace reader
+}  // namespace tint