OBS, demo recordings, and Shadowplay have always been the main programs used to record gameplay as far as I am aware.
Highly recommend Nvidia graphics cards for their shadowplay software. Shadowplay is unique because it allows you to in a press of a key record the last 2-10 minutes of gameplay. So it's like you're always recording, but you're only saving the content that you want.
I believe AMD has (or had) a similar thing they made recently, I forget the name but a small bit of searching could find it my dude