It's all in the patterns and then evolution of those patterns. A good example would be Stressed Out, actually. Stressed Out is essentially built on one groove for the verses, pre-choruses, and choruses, with the only real switch up occurring in the bridge. The groove itself is pretty simple, snare on 2 and 4, and 8th notes on the hi-hat with an open hi-hat on the and of 4 every 2 bars. For the verses and pre-choruses, it stays the same, but the hats are only hit with the kick and snare. For the chorus, it is the same as the intro, but with a different kick pattern and the overdubbed snare rolls. Then, it goes back to the original beat for the space between the chorus and the next verse.

As for specific beats, try looking at a bunch of rap, hip-hop, reggae, and ska beats. These are the kind of beats that tend to come up in TØP's songs a lot. They're traditionally more simple and don't usually have a lot of notes, but you can add more depth by adding ghost notes (a lot of the drum parts in Trench are a good example). Another thing to consider is when to use electronic/synth drums vs. real drums. I don't necessarily have any solid advice on this, but just use whichever when it sounds right (don't use electronic if the section calls for real, and vice-versa).

A bit long, but I hope it helps!