Cancer progression in humans is difficult to infer because we do not routinely sample patients at multiple stages of their disease. However, heterogeneous breast tumors provide a unique opportunity to study human tumor progression because they still contain evidence of early and intermediate subpopulations in the form of the phylogenetic relationships. We developed a method we call Sector-Ploidy-Profiling to study the clonal composition of breast tumors. SPP involves macro-dissecting tumors, flow-sorting genomic subpopulations by DNA content, and profiling genomes using comparative genomic hybridization. Breast carcinomas display two classes of genomic structural variation: (1) monogenomic and (2) polygenomic. Monogenomic tumors appear to contain a single major clonal subpopulation with a highly stable chromosome structure. Polygenomic tumors contain multiple clonal tumor subpopulations, which may occupy the same sectors, or separate anatomic locations. In polygenomic tumors, we show that heterogeneity can be ascribed to a few clonal subpopulations, rather than a series of gradual intermediates. While very informative, the SPP method yields only approximate results when applied to mixed populations of rapidly evolving cells. In such cases our understanding would be improved by dissecting genetic events at the single cell level. We therefore developed a method to quantify genomic copy number in single cells using next-generation sequencing. This method, single nucleus sequencing (SNS), involves flow-sorting single nuclei, whole genome amplification and sequencing random DNA fragments. We validated our method in a normal fibroblast cell line that has been deep-sequenced along with a genetically complex breast cancer cell line. We then used SNS to analyze 100 single cells isolated from a heterogeneous basal-like breast carcinoma. From this data, we constructed a detailed phylogenetic lineage, showing that the majority of cells belong to one of five major clonal subpopulations. Additionally, we observed a subpopulation of pseudodiploid cells with random amplifications and deletions that are not present in the major aneuploid subpopulations and may represent an unstable precursor. Our data support a model of tumor progression by sequential clonal expansions to form the mass of the tumor.