Quad-Tree

I've been searching around for the logic behind QuadTrees, and trying to implement my own QuadTree algorithm.  What's the basic logic behind QuadTrees?

It's like any tree, except instead of k number of children at non-leaf nodes, there are 4 children. So you use the same algorithms for traversing trees in general. In graphics or physics simulations, where it is used to partition space into a tree structure for logarithmic searches and culling, each non-leaf node in a tree represents the axis-aligned bounding volume of it's 4 children, in a recursive manner. That's all there is to it.