diff --git a/docs/design/README.md b/docs/design/README.md
index 26a0e3a7fa288..59a6f1048430f 100644
--- a/docs/design/README.md
+++ b/docs/design/README.md
@@ -3793,7 +3793,11 @@ the critical underpinnings of such abstractions.
 
 #### Lambdas
 
-> **TODO:**
+> **TODO:** References need to be evolved. Needs a detailed design and a high
+> level summary provided inline.
+
+> References: [Lambdas](lambdas.md),
+> [Proposal #3848: Lambdas](https://github.com/carbon-language/carbon-lang/pull/3848)
 
 #### Co-routines
 
diff --git a/docs/design/lambdas.md b/docs/design/lambdas.md
new file mode 100644
index 0000000000000..efaf51cbc4dcb
--- /dev/null
+++ b/docs/design/lambdas.md
@@ -0,0 +1,487 @@
+# Lambdas
+
+<!--
+Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+Exceptions. See /LICENSE for license information.
+SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+-->
+
+<!-- toc -->
+
+## Table of contents
+
+-   [Syntax Overview](#syntax-overview)
+    -   [Return type](#return-type)
+        -   [Return expression](#return-expression)
+        -   [Explicit return type](#explicit-return-type)
+        -   [No return](#no-return)
+    -   [Implicit parameters in square brackets](#implicit-parameters-in-square-brackets)
+    -   [Parameters](#parameters)
+    -   [Syntax defined](#syntax-defined)
+-   [Positional parameters](#positional-parameters)
+    -   [Positional parameter restrictions](#positional-parameter-restrictions)
+-   [Captures](#captures)
+    -   [Capture modes](#capture-modes)
+    -   [Default capture mode](#default-capture-mode)
+-   [Function fields in lambdas](#function-fields-in-lambdas)
+-   [Copy semantics](#copy-semantics)
+-   [Self and recursion](#self-and-recursion)
+-   [Alternatives considered](#alternatives-considered)
+
+<!-- tocstop -->
+
+## Syntax Overview
+
+One goal of Carbon's lambda syntax is to have continuity between lambdas and
+function declarations. Below are some example declarations:
+
+Implicit return types:
+
+```carbon
+// In a variable:
+let lambda: auto = fn => T.Make();
+// Equivalent in C++23:
+// const auto lambda = [] { return T::Make(); };
+
+// As an argument to a function call:
+Foo(10, 20, fn => T.Make());
+// Equivalent in C++23:
+// Foo(10, 20, [] { return T::Make(); });
+```
+
+Explicit return types:
+
+```carbon
+// In a variable:
+let lambda: auto = fn -> T { return T.Make(); };
+// Equivalent in C++23:
+// const auto lambda = [] -> T { return T::Make(); };
+
+// As an argument to a function call:
+PushBack(my_list, fn -> T { return T.Make() });
+// Equivalent in C++23:
+// PushBack(my_list, [] { return T::Make(); });
+```
+
+### Return type
+
+There are three options for how a lambda expresses its return type, parallel to
+[how function declarations express returns](functions.md#return-clause): using a
+return expression, using an explicit return type, or having no return.
+
+#### Return expression
+
+A return expression is introduced with a double arrow (`=>`) followed by an
+expression describing the function's return value. In this case, the return type
+is determined by the type of the expression, as if the return type was `auto`.
+
+```carbon
+// In a variable:
+let lambda: auto = fn => T.Make();
+// Equivalent in C++23:
+// const auto lambda = [] { return T::Make(); };
+
+// As an argument to a function call:
+Foo(fn => T.Make());
+// Equivalent in C++23:
+// Foo([] { return T::Make(); });
+```
+
+#### Explicit return type
+
+An explicit return type is introduced with a single arrow (`->`), followed by
+the return type, and finally the body of the lambda with a sequence of
+statements enclosed in curly braces (`{`...`}`).
+
+```carbon
+// In a variable:
+let lambda: auto = fn -> T { return T.Make(); };
+// Equivalent in C++23:
+// const auto lambda = [] -> T { return T::Make(); };
+
+// As an argument to a function call:
+Foo(fn -> T { return T.Make(); });
+// Equivalent in C++23:
+// Foo([] -> T { return T::Make(); });
+```
+
+#### No return
+
+Lambdas that don't return anything end with a body of statements in curly braces
+(`{`...`}`).
+
+```carbon
+// In a variable:
+let lambda: auto = fn { Print(T.Make()); };
+// Equivalent in C++23:
+// const auto lambda = [] -> void { Print(T::Make()); };
+
+// As an argument to a function call:
+Foo(fn { Print(T.Make()); });
+// Equivalent in C++23:
+// Foo([] -> void { Print(T::Make()); });
+```
+
+### Implicit parameters in square brackets
+
+Lambdas support [captures](#captures), [fields](#function-fields-in-lambdas) and
+deduced parameters in the square brackets.
+
+```carbon
+fn Foo(x: i32) {
+  // In a variable:
+  let lambda: auto = fn [var x, var y: i32 = 0] { Print(++x, ++y); };
+  // Equivalent in C++23:
+  // const auto lambda = [x, y = int32_t{0}] mutable -> void { Print(++x, ++y); };
+
+  // As an argument to a function call:
+  Foo(fn [var x, var y: i32 = 0] { Print(++x, ++y); });
+  // Equivalent in C++23:
+  // Foo([x, y = int32_t{0}] mutable -> void { Print(++x, ++y); });
+}
+```
+
+### Parameters
+
+Lambdas also support so-called ["positional parameters"](#positional-parameters)
+that are defined at their point of use using a dollar sign and a non-negative
+integer. They are implicitly of type `auto`.
+
+```carbon
+fn Foo() {
+  let lambda: auto = fn { Print($0); };
+  // Equivalent in C++23:
+  // auto lambda = [](auto _0, auto...) -> void { Print(_0); };
+  // Equivalent in Swift:
+  // let lambda = { Print($0) };
+}
+```
+
+Of course, lambdas can also have named parameters, but a single lambda can't
+have both named and positional parameters.
+
+```carbon
+fn Foo() {
+  // In a variable:
+  let lambda: auto = fn (v: auto) { Print(v); };
+  // Equivalent in C++23:
+  // const auto lambda = [](v: auto) -> void { Print(v); };
+
+  // As an argument to a function call:
+  Foo(fn (v: auto) { Print(v); });
+  // Equivalent in C++23:
+  // Foo([](v: auto) { Print(v); });
+}
+```
+
+And in additional the option between positional and named parameters, deduced
+parameters are always permitted.
+
+```carbon
+fn Foo() {
+  let lambda: auto = fn [T:! Printable](t: T) { Print(t); };
+}
+```
+
+### Syntax defined
+
+Lambda expressions have one of the following syntactic forms (where items in
+square brackets are optional and independent):
+
+`fn`\[_implicit-parameters_\] \[_tuple-pattern_\] `=>` _expression_
+
+`fn` \[_implicit-parameters_\] \[_tuple-pattern_\] \[`->` _return-type_\] `{`
+_statements_ `}`
+
+The first form is a shorthand for the second: "`=>` _expression_" is equivalent
+to "`-> auto { return` _expression_ `; }`".
+
+_implicit-parameters_ consists of square brackets enclosing a optional default
+capture mode and any number of explicit captures, function fields, and deduced
+parameters, all separated by commas. The default capture mode (if any) must come
+first; the other items can appear in any order. If _implicit-parameters_ is
+omitted, it is equivalent to `[]`.
+
+Function definitions are distinguished from lambdas by the presence of a name
+after the `fn` keyword.
+
+The presence of _tuple-pattern_ determines whether the function body uses named
+or positional parameters.
+
+The presence of "`->` _return-type_" determines whether the function body can
+(and must) return a value.
+
+To understand how the syntax between lambdas and function declarations is
+reasonably "continuous", refer to this table of syntactic positions and the
+following code examples.
+
+| Syntactic Position |                         Syntax Allowed in Given Position (optional, unless otherwise stated)                         |
+| :----------------: | :------------------------------------------------------------------------------------------------------------------: |
+|         A1         |                Required Returned Expression ([positional parameters](#positional-parameters) allowed)                |
+|         A2         |              Required Returned Expression ([positional parameters](#positional-parameters) disallowed)               |
+|         B          |                                    [Default capture mode](#default-capture-mode)                                     |
+|         C          | Explicit [Captures](#captures), [Function fields](#function-fields-in-lambdas) and Deduced Parameters (in any order) |
+|         D          |                                                 Explicit Parameters                                                  |
+|         E1         |            Body of Statements (no return value) ([positional parameters](#positional-parameters) allowed)            |
+|         E2         |           Body of Statements (with return value) ([positional parameters](#positional-parameters) allowed)           |
+|         E3         |          Body of Statements (no return value) ([positional parameters](#positional-parameters) disallowed)           |
+|         E4         |         Body of Statements (with return value) ([positional parameters](#positional-parameters) disallowed)          |
+|         F          |                                                 Required Return Type                                                 |
+
+```carbon
+// Lambdas (all the following are in an expression context and are
+// themselves expressions)
+
+fn => A1
+
+fn [B, C] => A1
+
+fn (D) => A2
+
+fn [B, C](D) => A2
+
+fn { E1; }
+
+fn -> F { E2; }
+
+fn [B, C] { E1; }
+
+fn [B, C] -> F { E2; }
+
+fn (D) { E3; }
+
+fn (D) -> F { E4; }
+
+fn [B, C](D) { E3; }
+
+fn [B, C](D) -> F { E4; }
+```
+
+## Positional parameters
+
+Positional parameters, denoted by a dollar sign followed by a non-negative
+integer (for example, $3), are auto-typed parameters defined within the lambda's
+body.
+
+```carbon
+let lambda: auto = fn => $0
+```
+
+They can be used in any lambda declaration that lacks an explicit parameter list
+(parentheses). They are variadic by design, meaning an unbounded number of
+arguments can be passed to any function that lacks an explicit parameter list.
+Only the parameters that are named in the body will be read from, meaning the
+highest named parameter denotes the minimum number of arguments required by the
+function. The lambda body is free to omit lower-numbered parameters (ex:
+`fn { Print($10); }`).
+
+This syntax was inpsired by Swift's
+[Shorthand Argument Names](https://docs.swift.org/swift-book/documentation/the-swift-programming-language/closures/#Shorthand-Argument-Names).
+
+```carbon
+// A lambda that takes two positional parameters being used as a comparator
+Sort(my_list, fn => $0.val < $1.val);
+// In Swift: { $0.val < $1.val }
+```
+
+### Positional parameter restrictions
+
+Lambdas with positional parameters have the restriction that they can only be
+used in a context where there is exactly one enclosing function or lambda that
+has no explicit parameter list. For example:
+
+```carbon
+fn Foo1 {
+  // ❌ Invalid: Foo1 is already using positional parameters
+  let lambda: auto = fn => $0 < $1
+}
+
+fn Foo2 {
+  my_list.Sort(
+    // ❌ Invalid: Foo2 is already using positional parameters
+    fn => $0 < $1
+  );
+}
+
+fn Foo3() {
+  my_list.Sort(
+    // ✅ Valid: Foo3 has explicit parameters
+    fn => $0 < $1
+  );
+}
+
+fn Foo4() {
+  let lambda: auto = fn -> bool {
+    // ❌ Invalid: Outer lambda is already using positional parameters
+    return (fn => $0 < $1)($0, $1);
+  };
+}
+
+fn Foo5() {
+  let lambda: auto = fn (x: i32, y: i32) -> bool {
+    // ✅ Valid: Outer lambda has explicit parameters
+    return (fn => $0 < $1)(x, y);
+  };
+}
+```
+
+## Captures
+
+Captures in Carbon mirror the non-init captures of C++. A capture declaration
+consists of a capture mode (for `var` captures) followed by the name of a
+binding from the enclosing scope, and makes that identifier available in the
+inner function body. The lifetime of a capture is the lifetime of the function
+in which it exists. For example...
+
+```carbon
+fn Foo() {
+  let handle: Handle = Handle.Get();
+  var thread: Thread = Thread.Make(fn [var handle] { handle.Process(); });
+  thread.Join();
+}
+```
+
+```carbon
+fn Foo() {
+  let handle: Handle = Handle.Get();
+  fn MyThread[handle]() { handle.Process(); }
+  var thread: Thread = Thread.Make(MyThread);
+  thread.Join();
+}
+```
+
+### Capture modes
+
+Lambdas can capture variables from their surrounding scope using `let` or `var`,
+just like regular bindings.
+
+Capture modes can be used as
+[default capture mode specifiers](#default-capture-mode) or for explicit
+captures as shown in the example code below.
+
+```carbon
+fn Example() {
+  var a: i32 = 0;
+  var b: i32 = 0;
+
+let lambda: auto = fn [a, var b] {
+  // ❌ Invalid: by-value captures are immutable (default `let`)
+  a += 1;
+  // ✅ Valid: `b` is a mutable copy (captured with `var`)
+  b += 1;
+};
+
+  lambda();
+}
+```
+
+```carbon
+fn Example {
+  fn Invalid() -> auto {
+    var s: String = "Hello world";
+    return fn [s]() => s;
+  }
+
+  // ❌ Invalid: returned lambda references `s` which is no longer alive
+  // when the lambda is invoked.
+  Print(Invalid()());
+}
+```
+
+Note: If a function object F has mutable state, either because it has a
+by-object capture or because it has a by-object function field, then a call to F
+should require the callee to be a reference expression rather than a value
+expression. We need a mutable handle to the function in order to be able to
+mutate its mutable state.
+
+### Default capture mode
+
+By default, there is no capturing in lambdas. The lack of any square brackets is
+the same as an empty pair of square brackets. Users can opt into capturing
+behavior. This is done either by way of individual explicit captures, or more
+succinctly by way of a default capture mode. The default capture mode roughly
+mirrors the syntax `[=]` and `[&]` capture modes from C++ by being the first
+thing to appear in the square brackets.
+
+```carbon
+fn Foo1() {
+  let handle: Handle = Handle.Get();
+  fn MyThread[var]() {
+    // `handle` is captured by-object due to the default capture
+    // mode specifier of `var`
+    handle.Process();
+  }
+  var thread: Thread = Thread.Make(MyThread);
+  thread.Join();
+}
+
+fn Foo2() {
+  let handle: Handle = Handle.Get();
+  fn MyThread[let]() {
+    // `handle` is captured by-value due to the default capture
+    // mode specifier of `let`
+    handle.Process();
+  }
+  var thread: Thread = Thread.Make(MyThread);
+  thread.Join();
+}
+```
+
+## Function fields in lambdas
+
+Function fields in lambdas mirror the behavior of init captures in C++. A
+function field definition consists of an irrefutable pattern, `=`, and an
+initializer. It matches the pattern with the initializer when the lambda
+definition is evaluated. The bindings in the pattern have the same lifetime as
+the function, and their scope extends to the end of the function body.
+
+```carbon
+fn Foo() {
+  var h1: Handle = Handle.Get();
+  var h2: Handle = Handle.Get();
+  var thread: Thread = Thread.Make(fn [a: auto = h1, var b: auto = h2] {
+    a.Process();
+    b.Process();
+  });
+  thread.Join();
+}
+```
+
+## Copy semantics
+
+To mirror the behavior of C++, lambdas will be as copyable as their contained
+function fields and function captures. This means that, if a function holds a
+by-object function field, if the type of the field is copyable, so too is the
+function that contains it. This also applies to captures.
+
+The other case is by-value function fields. Since C++ const references, when
+made into fields of a class, prevent the class from being copied assigned, so
+too should by-value function fields prevent the function in which it is
+contained from being copied assigned.
+
+## Self and recursion
+
+To mirror C++'s use of capturing `this`, `self` should always come from the
+outer scope as a capture. `self: Self` is never permitted on lambdas.
+
+```carbon
+// ❌ Not allowed
+let lambda: auto = fn [self: Self] { self.F(); };
+
+// ✅ Captures `self` from outer scope
+let lambda: auto = fn [self] { self.F(); };
+```
+
+Note: Following
+[#3720](https://github.com/carbon-language/carbon-lang/pull/3720), an expression
+of the form `x.(F)`, where `F` is a function with a `self` or `addr self`
+parameter, produces a callable that holds the value of `x`, and does not hold
+the value of `F`. As a consequence, we can't support combining captures and
+function fields with a `self` parameter.
+
+## Alternatives considered
+
+-   [Terse vs Elaborated](/proposals/p3848.md#alternative-considered-terse-vs-elaborated)
+-   [Sigil](/proposals/p3848.md#alternative-considered-sigil)
+-   [Additional Positional Parameter Restriction](/proposals/p3848.md#alternative-considered-additional-positional-parameter-restriction)
+-   [Recursive Self](/proposals/p3848.md#alternative-considered-recursive-self)