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.