Another technique that helps is to limit the amount of information shared with clients to need to know info. This can be computationally intensive server-side and hard to get right .. but it can help in many cases. There are evolving techniques to do this.

In FPS games, there can also be streaming input validation. eg. Accurate fire requires the right sequence of events and/or is used for cheat detection. At the point where cheats have to emulate human behaviour, with human-like reaction times, the value of cheating drops.

That's the advanced stuff. Many games don't even check whether people are running around out of bounds, flying through the air etc. Known bugs and map exploits don't get fixed for years.