Cancer progression is driven by mutation and selection in an asexually reproducing population of tumor cells. We present mathematical models for the genetic progression of cancer. A statistical model is introduced to describe the ordered accumulation of mutations in cancer genomes and shown to improve survival predictions for patients with renal cell carcinoma. We analyze the evolutionary dynamics of tumor progression using a population genetics approach and present statistical methods for inferring the genetic diversity of tumor cell populations from ultra-deep sequencing experiments based on detecting subclonal single-nucleotide variants.