Composite Dilation Wavelets were introduced by Guo, Labate, Lim, Weiss, and Wilson as a new class of wavelets with multiple dilation matrices. These wavelets expand upon Shearlets and include, among others, crystallographic wavelets. We will discuss the extensions of standard multi-scale theory along with constructions of compactly supported composite dilation frames. We will also present a few applications along with fast numerical algorithms.