You can now mirror the screen from select Android and Windows mobile devices onto your TV via a Roku 3 box or Roku streaming stick. However, it is still a beta feature.
Roku screen mirroing
Roku has far more apps and content than the Apple TV, but for years Apple TV has offered the excellent Airplay and Airplay Mirroring features. Roku is now adding similar mirroring functionality to its boxes, in addition to the “Play On Roku” feature that is already available.

Screen mirroring will let you mirror the screen – for example video, photos or music - from an Android or Windows device onto the TV screen. You need either a Roku 3 or the latest version of the Roku Streaming Stick. You also need a recent mobile device, as only a select few are supported right now.
The mirror functionality appears to be based on Miracast, so if you own a mobile device with Miracast it should work. However, Roku only guarantees compatibility with the devices on this list.
The beta update is rolling out to Roku players today so check for an update.