By far, most evolutionary research has focused on the changes that occur in the germline of individuals across generations, within and between species. For different reasons, much less attention has been given to the process of change within the somatic line of a multicellular individual. The formation of cancer tumors due to uncontrolled cell proliferation is one of the most prominent forms of somatic evolution. The evolution of cancer tumors in a body can be likened with the evolution of populations in more or less fragmented habitats. The tumor is usually a expanding population of clonal cells, which may differentiate to a bigger or lesser extent (population structure) and disperse to contiguous (range expansion) or more distant tissues (long distance colonization). During tumor progression, this population of cells is subject to distinct somatic evolutionary processes like mutation, drift, selection or migration, which can act at different points in time and geographical space. Very recently, the discovery of extensive intratumor heterogeneity, together with the rise of single cell genomics, has created an unique opportunity to study the phylogeography of cancer tumor cells. So far evolutionary inferences drawn from cancer genomes have been mostly qualitative. Here we propose to study a thousand single cell genomes from different regions in primary tumors and matched metastases. We will develop and apply state-of-the-art statistical and computational techniques from phylogenetics, phylogeography and population genomics to understand the tempo and mode of evolution of cell lineages within and between cancer tumors. By doing so we aim to construct a robust theoretical and methodological evolutionary framework that can contribute to a better understanding of the process of somatic evolution and shed light into the biology of cancer.