I understand how box collision, sphere collision, and other such collisions work. However, how would one implement realistic 3D collisions? That is, objects would interact with one another as they would in real life. For example, take a rod and a torus. Assume that the thickness of the rod is smaller than the hole in the torus. With simple collision systems, as far as I know, inserting the rod into the hole of the torus would result in a collision detection. In reality, no collision would take place. Hopefully, that explains what I am looking for.
You can compound various primitives together to add accuracy to your collision model. For instance in your torus example, you could have a bounding box or sphere around the entire model but then also have a sphere that just encompasses the torus' hole. Then the algo would go: if rod is in box but not in holeSphere, then it's colliding, else if rod is in box and holeSphere, it is not colliding.
You can often use a few basic primitives (planes, rays, boxes, spheres) together to get an acceptable level of accuracy.
Definitely get 'Real time collision detection' by Chtister Ericsson,.