Deep genome sequencing is now providing extensive catalogues of somatic mutations and their frequencies in tumors. These data have stimulated the development of mathematical inference methods for elucidating how genetic evolution and clonal growth of cancers are intertwined. Here, we review recent progress in this field that has shed light on early mutational events linked to tumor origins and subsequent paths of selective or neutral evolution of tumors. These techniques also enable quantification of the selective advantage of oncogenic driver mutations. Collectively, the modeling approaches now allow us to infer key dynamic processes of tumor development from somatic mutation patterns.