I recently implemented in my new 3D engine, called PATRIA (developed for my development team http://teamnovasoft.com) a new collision system based on Collision spheres.
I decided to use the sphere system in place of the more costly AABB system in order to have a simple and perfomant collision system and not introduce any additional overhead to the whole engine.
I have to keep into consideration that the engine must be fast enought to run on mobile platforms and there, for obvious reasons, the available resources are very limited.
The logic behind this system is that the information to be kept to define a sphere in a 3D space is very basic, the coordinate of the center (3 floats, x, y and z coordinates) and the size of the radius of the sphere.
Having said so, if I have 2 spheres, in order to determine if the spheres and under collision, it is suffice to calculate the distance of the centers and see if the distance is longer of shorter than the sum of the 2 radius.
I have created another video to show you a more dedicated explanation of the logic applied: