I will discuss my group's long-term effort to develop multiscale graph basis dictionaries that generalize the classical counterparts: wavelet packet and local cosine basis dictionaries. After briefly reviewing the classical wavelet packets and local cosine basis dictionaries, I plan to describe the difficulties of lifting those to the graph setting, and how we could overcome them. There are two keys for successful constructions: 1) hierarchical bipartition tree of a given graph; and 2) the concept of the "dual" domain of a graph. I will first discuss the simplest of all, the Hierarchical Graph Laplacian Eigen Transform (HGLET) that corresponds to the classical hierarchical block discrete cosine transform. Second, I will describe our idea of generating the dual domain of a given graph based on the geometry of graph Laplacian eigenvectors, and subsequently discuss the Natural Graph Wavelet Packets (NGWPs), which is a generalization of the Shannon wavelet packets. I will conclude my talk with my perspective on these tools, our future plans including how to deal with directed graphs, and the information on our software package of these dictionaries completely written in the Julia programming language.