diff --git a/internal/encoding/messageset/messageset.go b/internal/encoding/messageset/messageset.go
index 837e5c4..9d22dd7 100644
--- a/internal/encoding/messageset/messageset.go
+++ b/internal/encoding/messageset/messageset.go
@@ -61,9 +61,13 @@
 // In text and JSON formats, the extension name used is the message itself.
 // The extension field name is derived by appending ExtensionName.
 func FindMessageSetExtension(r preg.ExtensionTypeResolver, s pref.FullName) (pref.ExtensionType, error) {
-	xt, err := r.FindExtensionByName(s.Append(ExtensionName))
+	name := s.Append(ExtensionName)
+	xt, err := r.FindExtensionByName(name)
 	if err != nil {
-		return nil, err
+		if err == preg.NotFound {
+			return nil, err
+		}
+		return nil, errors.Wrap(err, "%q", name)
 	}
 	if !IsMessageSetExtension(xt.TypeDescriptor()) {
 		return nil, preg.NotFound
diff --git a/internal/errors/errors.go b/internal/errors/errors.go
index bc495b4..20c17b3 100644
--- a/internal/errors/errors.go
+++ b/internal/errors/errors.go
@@ -6,20 +6,19 @@
 package errors
 
 import (
+	"errors"
 	"fmt"
 
 	"google.golang.org/protobuf/internal/detrand"
 )
 
+// Error is a sentinel matching all errors produced by this package.
+var Error = errors.New("protobuf error")
+
 // New formats a string according to the format specifier and arguments and
 // returns an error that has a "proto" prefix.
 func New(f string, x ...interface{}) error {
-	for i := 0; i < len(x); i++ {
-		if e, ok := x[i].(*prefixError); ok {
-			x[i] = e.s // avoid "proto: " prefix when chaining
-		}
-	}
-	return &prefixError{s: fmt.Sprintf(f, x...)}
+	return &prefixError{s: format(f, x...)}
 }
 
 type prefixError struct{ s string }
@@ -38,6 +37,49 @@
 	return prefix + e.s
 }
 
+func (e *prefixError) Unwrap() error {
+	return Error
+}
+
+// Wrap returns an error that has a "proto" prefix, the formatted string described
+// by the format specifier and arguments, and a suffix of err. The error wraps err.
+func Wrap(err error, f string, x ...interface{}) error {
+	return &wrapError{
+		s:   format(f, x...),
+		err: err,
+	}
+}
+
+type wrapError struct {
+	s   string
+	err error
+}
+
+func (e *wrapError) Error() string {
+	return format("%v%v: %v", prefix, e.s, e.err)
+}
+
+func (e *wrapError) Unwrap() error {
+	return e.err
+}
+
+func (e *wrapError) Is(target error) bool {
+	return target == Error
+}
+
+func format(f string, x ...interface{}) string {
+	// avoid "proto: " prefix when chaining
+	for i := 0; i < len(x); i++ {
+		switch e := x[i].(type) {
+		case *prefixError:
+			x[i] = e.s
+		case *wrapError:
+			x[i] = format("%v: %v", e.s, e.err)
+		}
+	}
+	return fmt.Sprintf(f, x...)
+}
+
 func InvalidUTF8(name string) error {
 	return New("field %v contains invalid UTF-8", name)
 }
diff --git a/internal/errors/errors_test.go b/internal/errors/errors_test.go
index b489edd..804eb96 100644
--- a/internal/errors/errors_test.go
+++ b/internal/errors/errors_test.go
@@ -5,27 +5,63 @@
 package errors
 
 import (
+	"errors"
 	"strings"
 	"testing"
 )
 
-func TestNewPrefix(t *testing.T) {
-	e1 := New("abc")
-	got := e1.Error()
-	if !strings.HasPrefix(got, "proto:") {
-		t.Errorf("missing \"proto:\" prefix in %q", got)
-	}
-	if !strings.Contains(got, "abc") {
-		t.Errorf("missing text \"abc\" in %q", got)
-	}
-
-	e2 := New("%v", e1)
-	got = e2.Error()
-	if !strings.HasPrefix(got, "proto:") {
-		t.Errorf("missing \"proto:\" prefix in %q", got)
-	}
-	// Test to make sure prefix is removed from the embedded error.
-	if strings.Contains(strings.TrimPrefix(got, "proto:"), "proto:") {
-		t.Errorf("prefix \"proto:\" not elided in embedded error: %q", got)
+func TestErrors(t *testing.T) {
+	var sentinel = New("sentinel")
+	var foreign = errors.New("foreign")
+	for _, test := range []struct {
+		what     string
+		err      error
+		wantText string
+		is       []error
+		isNot    []error
+	}{{
+		what:     `New("abc")`,
+		err:      New("abc"),
+		wantText: "abc",
+	}, {
+		what:     `New("%v", sentinel)`,
+		err:      New("%v", sentinel),
+		wantText: "sentinel",
+		isNot:    []error{sentinel},
+	}, {
+		what:     `Wrap(sentinel, "%v", "text")`,
+		err:      Wrap(sentinel, "%v", "text"),
+		wantText: "text: sentinel",
+		is:       []error{sentinel},
+	}, {
+		what:     `New("%v", foreign)`,
+		err:      New("%v", foreign),
+		wantText: "foreign",
+		isNot:    []error{foreign},
+	}, {
+		what:     `Wrap(foreign, "%v", "text")`,
+		err:      Wrap(foreign, "%v", "text"),
+		wantText: "text: foreign",
+		is:       []error{foreign},
+	}} {
+		if got, want := test.err.Error(), prefix; !strings.HasPrefix(got, want) {
+			t.Errorf("%v.Error() = %q, want prefix %q", test.what, got, want)
+		}
+		if got, want := test.err.Error(), prefix+test.wantText; got != want {
+			t.Errorf("%v.Error() = %q, want %q", test.what, got, want)
+		}
+		if got, want := Is(test.err, Error), true; got != want {
+			t.Errorf("errors.Is(%v, errors.Error) = %v, want %v", test.what, got, want)
+		}
+		for _, err := range test.is {
+			if got, want := Is(test.err, err), true; got != want {
+				t.Errorf("errors.Is(%v, %v) = %v, want %v", test.what, err, got, want)
+			}
+		}
+		for _, err := range test.isNot {
+			if got, want := Is(test.err, err), false; got != want {
+				t.Errorf("errors.Is(%v, %v) = %v, want %v", test.what, err, got, want)
+			}
+		}
 	}
 }
diff --git a/internal/errors/is_go112.go b/internal/errors/is_go112.go
new file mode 100644
index 0000000..0f5e585
--- /dev/null
+++ b/internal/errors/is_go112.go
@@ -0,0 +1,42 @@
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build !go1.13
+
+package errors
+
+import "reflect"
+
+// Is is a copy of Go 1.13's errors.Is for use with older Go versions.
+func Is(err, target error) bool {
+	if target == nil {
+		return err == target
+	}
+
+	isComparable := reflect.TypeOf(target).Comparable()
+	for {
+		if isComparable && err == target {
+			return true
+		}
+		if x, ok := err.(interface{ Is(error) bool }); ok && x.Is(target) {
+			return true
+		}
+		// TODO: consider supporing target.Is(err). This would allow
+		// user-definable predicates, but also may allow for coping with sloppy
+		// APIs, thereby making it easier to get away with them.
+		if err = unwrap(err); err == nil {
+			return false
+		}
+	}
+}
+
+func unwrap(err error) error {
+	u, ok := err.(interface {
+		Unwrap() error
+	})
+	if !ok {
+		return nil
+	}
+	return u.Unwrap()
+}
diff --git a/internal/errors/is_go113.go b/internal/errors/is_go113.go
new file mode 100644
index 0000000..dc05f41
--- /dev/null
+++ b/internal/errors/is_go113.go
@@ -0,0 +1,12 @@
+// Copyright 2020 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build go1.13
+
+package errors
+
+import "errors"
+
+// Is is errors.Is.
+func Is(err, target error) bool { return errors.Is(err, target) }
diff --git a/internal/impl/decode.go b/internal/impl/decode.go
index a2993d4..6e78faa 100644
--- a/internal/impl/decode.go
+++ b/internal/impl/decode.go
@@ -189,7 +189,7 @@
 			if err == preg.NotFound {
 				return out, errUnknown
 			}
-			return out, err
+			return out, errors.New("%v: unable to resolve extension %v: %v", mi.Desc.FullName(), num, err)
 		}
 	}
 	xi := getExtensionFieldInfo(xt)
diff --git a/proto/decode.go b/proto/decode.go
index d8b9187..b712786 100644
--- a/proto/decode.go
+++ b/proto/decode.go
@@ -124,7 +124,7 @@
 		if fd == nil && md.ExtensionRanges().Has(num) {
 			extType, err := o.Resolver.FindExtensionByNumber(md.FullName(), num)
 			if err != nil && err != protoregistry.NotFound {
-				return err
+				return errors.New("%v: unable to resolve extension %v: %v", md.FullName(), num, err)
 			}
 			if extType != nil {
 				fd = extType.TypeDescriptor()
diff --git a/proto/messageset.go b/proto/messageset.go
index e27e0b7..f9af2ad 100644
--- a/proto/messageset.go
+++ b/proto/messageset.go
@@ -78,7 +78,7 @@
 		return errUnknown
 	}
 	if err != nil {
-		return err
+		return errors.New("%v: unable to resolve extension %v: %v", md.FullName(), num, err)
 	}
 	xd := xt.TypeDescriptor()
 	if err := o.unmarshalMessage(v, m.Mutable(xd).Message()); err != nil {
diff --git a/proto/proto.go b/proto/proto.go
index 983fc71..1fec109 100644
--- a/proto/proto.go
+++ b/proto/proto.go
@@ -5,8 +5,19 @@
 package proto
 
 import (
+	"google.golang.org/protobuf/internal/errors"
 	"google.golang.org/protobuf/reflect/protoreflect"
 )
 
 // Message is the top-level interface that all messages must implement.
 type Message = protoreflect.ProtoMessage
+
+// Error matches all errors produced by packages in the protobuf module.
+//
+// That is, errors.Is(err, Error) reports whether an error is produced
+// by this module.
+var Error error
+
+func init() {
+	Error = errors.Error
+}
diff --git a/reflect/protodesc/desc_resolve.go b/reflect/protodesc/desc_resolve.go
index 1bf4799..cebb36c 100644
--- a/reflect/protodesc/desc_resolve.go
+++ b/reflect/protodesc/desc_resolve.go
@@ -187,7 +187,7 @@
 			}
 			foundButNotImported = d
 		} else if err != protoregistry.NotFound {
-			return nil, err
+			return nil, errors.Wrap(err, "%q", s)
 		}
 
 		// Continue on at a higher level of scoping.
diff --git a/reflect/protoregistry/registry.go b/reflect/protoregistry/registry.go
index c77f77a..8385c75 100644
--- a/reflect/protoregistry/registry.go
+++ b/reflect/protoregistry/registry.go
@@ -47,6 +47,9 @@
 var GlobalTypes *Types = new(Types)
 
 // NotFound is a sentinel error value to indicate that the type was not found.
+//
+// Since registry lookup can happen in the critical performance path, resolvers
+// must return this exact error value, not an error wrapping it.
 var NotFound = errors.New("not found")
 
 // Files is a registry for looking up or iterating over files and the