Composite dilation wavelets are a class of directional multi scale representations developed by K. Guo, D. Labate, W.-Q. Lim, G. Weiss, and E. Wilson. They are a class of basis generated by the action of a lattice group and dilations from a set of matrices $B$. In particular, this class includes shearlets when $B$ is a group of shearing matrices. We will focus on composite dilation wavelets with finite group $B$ and, unlike the shearlet case, is non-commutative. These type of wavelets can be thought of as usual wavelets except the group of integer translates $\mathbb{Z}$ is replaced with a non-commutative group.We will mention the contributions to the theory of these type of wavelets along with constructions of MRA composite wavelets.