I did a simple game where I rolled my own physics and collision detection. It only had to deal with rectangles so the math should have been fairly simple, but

I did a simple game where I rolled my own physics and collision detection. It only had to deal with rectangles so the math should have been fairly simple, but I had a bit of a hard time with things like detecting which side/face was being collided with, dealing with slight overlaps, and handling all the different edge cases. I'm sure it gets much harder with more shapes and dimensions, but also easier if you just want to detect any overlap and not "resolve" the collision physics.