Systematic studies of cancer genomes have provided unprecedented insights into the molecular nature of cancer. Using this information to guide the development and application of therapies in the clinic is challenging. Here, we report how cancer-driven alterations identified in 11,289 tumors from 29 tissues (integrating somatic mutations, copy number alterations, DNA methylation, and gene expression) can be mapped onto 1,001 molecularly annotated human cancer cell lines and correlated with sensitivity to 265 drugs. We find that cell lines faithfully recapitulate oncogenic alterations identified in tumors, find that many of these associate with drug sensitivity/resistance, and highlight the importance of tissue lineage in mediating drug response. Logic-based modeling uncovers combinations of alterations that sensitize to drugs, while machine learning demonstrates the relative importance of different data types in predicting drug response. Our analysis and datasets are rich resources to link genotypes with cellular phenotypes and to identify therapeutic options for selected cancer sub-populations.