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Updated
The DualShock PS4 Controller is a gaming controller made by Playstation for the PS4. It is able to work on PC through various third party apps that install drivers, mimicing the support of an Xbox controller.
Specs
Pros
Pro Game compatibility is increasing
Some recent games will work with the PS4 controller without the need of an app/driver to emulate the XBox controller, and you will see PS4 button prompts on the screen (cross, square, circle, triangle, etc.). Some example games are: The Division (Ubisoft), Rocket League and Paragon (Epic Games / Early Access).
Pro App available that offers many functions
In order to get easy wireless support as well as button mapping and loading of profiles the user can install a third party app called DS4Windows. While this is an extra step, the features it offers are worthwhile for anyone looking to get full compatibility with the controller.
Cons
Con Best compatibility requires an app on Windows
Out of the box support may not be that great with the PS4 controller on PC. Buttons may need to be mapped in order for the controller to work as intended. Only games with DirectInput support will work out of the box. This means the user will need to install button mapping software or some other app that allow gaming profiles to be loaded easily to get a similar experience to using an XBox controller.
Please note this only applies to Windows, which requires a wrapper such as DS4Windows for XInput support (and thus vibration and touchpad support). Linux supports all of the controller's features natively since kernel version 3.15.