Can I use an Xbox 360 controller to play Xbox One?

The Xbox One cannot directly accept input from an Xbox 360 controller - however, with Windows 10, there is a work around.

Windows 10 allows you to set up your Xbox One to stream to your computer. While streaming to your computer, you are directed to connect the controller into the computer, not the Xbox One.

In this form, Xbox 360 controllers will work for playing Xbox One games. You can directly plug in a wired controller, or use an adapter, if you are using the wireless controllers.