Valve tried to radically redesign the gaming controller with its own Steam controller, but for a lot of players it never quite caught on. Fortunately, Steam is a very flexible OS and it's pretty easy to use your controller of choice. Like the PS4's Dualshock 4 controller, for example: Valve just announced today that the Steam client now fully supports the Dualshock 4. That means all the controller's capabilities can be mapped to various functions in Steam, including the trackpad and gyroscope.
Valve also notes the controllers will have access to the full range of APIs that Steam controllers have access to. There's a whole host of other controller feature additions in this update, as well. There are settings to control the LEDs on your controller (like the Dualshock 4 has), a joystick-controlled mouse, preferences for haptic feedback, and software-based gyroscope and accelerometer integration -- something that'll specifically add extended support for the PS4 controller's gyro input.