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Abstract: Cancer arises and evolves through the accumulation of somatic mutations which may provide a selective advantage. The interplay of mutations and their functional consequences shapes tumor progression and contributes to different clinical outcomes. Single-cell sequencing data enables a high-resolution characterization of this process, but requires powerful statistical models able to distinguish signal from noise. In this talk I discuss computational methods to analyze single-cell sequencing data from tumors to reconstruct the evolution of cancer cells, map genomic to transcriptional changes, and characterize the complex cell type composition of the tumor microenvironment. We present novel statistical models to integrate single-cell transcriptomes with copy number evolutionary trees, and to find hierarchical gene signatures from single-cell RNA-sequencing data. These methods provide rich descriptions of intra-tumor heterogeneity which are fundamental for the understanding of its complex dynamics and the development of targeted therapies.