1) Officially Supported
• Mouse + Keyboard
• Microsoft Xbox 360
• Microsoft Xbox One
• Microsoft Xbox One Elite
• Sony Playstation 4

2) Semi-officially Supported (might require the installation of dedicated drivers)
• Any 3rd Party Xbox-Compatible Controller
• Logitech Chillstream
• Ouya Controller
• Steam Controller
• Sony PS3 Controller (Custom Drivers are publicly available)

3) Not officially supported (you can try but Your Mileage May Vary)
• Anything else (e.g. older DirectInput controllers)