Neoplastic progression and acquired therapeutic resistance in cancer proceed through a process of somatic evolution. The fact that somatic evolution drives these processes is well established. What has been unknown are the dynamics of that process. Recent work from our lab and others is starting to reveal some surprises. There are hints that progression may proceed through a dynamic of punctuated equilibrium. In addition, generating one sequence for the genome of a neoplasm obscures extensive genetic diversity at the cell level, which likely drives both progression and therapeutic resistance. I will describe how powerful tools from evolutionary biology can be brought to bear on the elucidation of these dynamics.