How should I customize DropdownButtons and DropdownMenuItems in Flutter?

The default DropdownButton with DropdownMenuItems returns a light-grey dropdown. How should I customize the dropdown (e.g. background color, dropdown width)? I can change the style property in both DropdownButton and DropdownMenuItem, like this:

return new DropdownButton(
      value: ...,
      items: ...,
      onChanged: ...,
      style: new TextStyle(
        color: Colors.white,
      ),
    );

but this doesn't change the dropdown's background color.

Should I copy DropdownMenu and extend it? Does Flutter plan to add customization for this widget in the near future?

As Collin said, your DropdownMenuItem will follow your ThemeData class. Not only its backgroundColor will match the canvasColor in your ThemeData class, but also it will follow the same TextStyle.

So, for a quick example:

new ThemeData(
        fontFamily: "Encode Sans", //my custom font
        canvasColor: _turquoise, //my custom color
//other theme data)

Furthermore, if you want to control the width of the menu, you can feed its child property a new Container and add the desired width, check the following GIF, I started with width: 100.0 then hot reloaded after changing it to 200.0, notice how the width was manipulated, just make sure you use a suitable width so that you do not get overflow problems later on when you use the menu within a more complex layout.

class TestPage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(
        title:new Text ("Test"),
      ),
      body: new Center(
        child: new DropdownButton(items: new List.generate(20, (int index){
          return new DropdownMenuItem(child: new Container(
            child: new Text ("Item#$index"),
            width: 200.0, //200.0 to 100.0
          ));
        })
            , onChanged: null)
      ),
    );
  }
}