diff --git a/Makefile b/Makefile
index 3dfc08a0e..46d40a7a9 100644
--- a/Makefile
+++ b/Makefile
@@ -5,22 +5,27 @@ export CGO_CFLAGS
 CGO_LDFLAGS ?= $(filter -g -L% -l% -O%,${LDFLAGS})
 export CGO_LDFLAGS
 
+EXE =
+ifeq ($(GOOS),windows)
+EXE = .exe
+endif
+
 ## The following tasks delegate to `script/build.go` so they can be run cross-platform.
 
-.PHONY: bin/gh
-bin/gh: script/build
-	@script/build bin/gh
+.PHONY: bin/gh$(EXE)
+bin/gh$(EXE): script/build
+	@script/build $@
 
 script/build: script/build.go
-	go build -o script/build script/build.go
+	GOOS= GOARCH= GOARM= GOFLAGS= CGO_ENABLED= go build -o $@ $<
 
 .PHONY: clean
 clean: script/build
-	@script/build clean
+	@script/build $@
 
 .PHONY: manpages
 manpages: script/build
-	@script/build manpages
+	@script/build $@
 
 # just a convenience task around `go test`
 .PHONY: test
diff --git a/docs/source.md b/docs/source.md
index 28c9a2312..17e6b0185 100644
--- a/docs/source.md
+++ b/docs/source.md
@@ -27,9 +27,9 @@
    ```
 
    #### Windows 
-   ```sh
+   ```pwsh
    # build the `bin\gh.exe` binary
-   > go run script/build.go
+   > go run script\build.go
    ```
    There is no install step available on Windows.
 
@@ -37,3 +37,23 @@
 
    #### Windows
    Run `bin\gh version` to check if it worked.
+
+## Cross-compiling binaries for different platforms
+
+You can use any platform with Go installed to build a binary that is intended for another platform
+or CPU architecture. This is achieved by setting environment variables such as GOOS and GOARCH.
+
+For example, to compile the `gh` binary for the 32-bit Raspberry Pi OS:
+```sh
+# on a Unix-like system:
+$ GOOS=linux GOARCH=arm GOARM=7 CGO_ENABLED=0 make clean bin/gh
+```
+```pwsh
+# on Windows, pass environment variables as arguments to the build script:
+> go run script\build.go clean bin\gh GOOS=linux GOARCH=arm GOARM=7 CGO_ENABLED=0
+```
+
+Run `go tool dist list` to list all supported values of GOOS/GOARCH.
+
+Tip: to reduce the size of the resulting binary, you can use `GO_LDFLAGS="-s -w"`. This omits
+symbol tables used for debugging. See the list of [supported linker flags](https://golang.org/cmd/link/).
diff --git a/script/build.go b/script/build.go
index 3d26ca7cb..2c92a5f20 100644
--- a/script/build.go
+++ b/script/build.go
@@ -1,6 +1,6 @@
 // Build tasks for the GitHub CLI project.
 //
-// Usage:  go run script/build.go [<task>]
+// Usage:  go run script/build.go [<tasks>...] [<env>...]
 //
 // Known tasks are:
 //
@@ -65,34 +65,54 @@ var tasks = map[string]func(string) error{
 var self string
 
 func main() {
-	task := "bin/gh"
-	if runtime.GOOS == "windows" {
-		task = "bin\\gh.exe"
+	args := os.Args[:1]
+	for _, arg := range os.Args[1:] {
+		if idx := strings.IndexRune(arg, '='); idx >= 0 {
+			os.Setenv(arg[:idx], arg[idx+1:])
+		} else {
+			args = append(args, arg)
+		}
 	}
 
-	if len(os.Args) > 1 {
-		task = os.Args[1]
+	if len(args) < 2 {
+		if isWindowsTarget() {
+			args = append(args, filepath.Join("bin", "gh.exe"))
+		} else {
+			args = append(args, "bin/gh")
+		}
 	}
 
-	self = filepath.Base(os.Args[0])
+	self = filepath.Base(args[0])
 	if self == "build" {
 		self = "build.go"
 	}
 
-	t := tasks[normalizeTask(task)]
-	if t == nil {
-		fmt.Fprintf(os.Stderr, "Don't know how to build task `%s`.\n", task)
-		os.Exit(1)
-	}
+	for _, task := range args[1:] {
+		t := tasks[normalizeTask(task)]
+		if t == nil {
+			fmt.Fprintf(os.Stderr, "Don't know how to build task `%s`.\n", task)
+			os.Exit(1)
+		}
 
-	err := t(task)
-	if err != nil {
-		fmt.Fprintln(os.Stderr, err)
-		fmt.Fprintf(os.Stderr, "%s: building task `%s` failed.\n", self, task)
-		os.Exit(1)
+		err := t(task)
+		if err != nil {
+			fmt.Fprintln(os.Stderr, err)
+			fmt.Fprintf(os.Stderr, "%s: building task `%s` failed.\n", self, task)
+			os.Exit(1)
+		}
 	}
 }
 
+func isWindowsTarget() bool {
+	if os.Getenv("GOOS") == "windows" {
+		return true
+	}
+	if runtime.GOOS == "windows" {
+		return true
+	}
+	return false
+}
+
 func version() string {
 	if versionEnv := os.Getenv("GH_VERSION"); versionEnv != "" {
 		return versionEnv