Advances in whole genome amplification and next-generation sequencing methods have enabled genomic analyses of single cells, and these techniques are now beginning to be used to detect genomic lesions in individual cancer cells. Previous approaches have been unable to resolve genomic differences in complex mixtures of cells, such as heterogeneous tumors, despite the importance of characterizing such tumors for cancer treatment. Sequencing of single cells is likely to improve several aspects of medicine, including the early detection of rare tumor cells, monitoring of circulating tumor cells (CTCs), measuring intratumor heterogeneity, and guiding chemotherapy. In this review we discuss the challenges and technical aspects of single-cell sequencing, with a strong focus on genomic copy number, and discuss how this information can be used to diagnose and treat cancer patients.