Cancer drug resistance is almost inevitable in the majority of patients with advanced metastatic tumours. Intra-tumour heterogeneity, facilitating rapid tumour evolution, is a main cause of resistance to cancer therapies. In this thesis, I explore how cancer genome sequencing data can shed light intratumour heterogeneity and the processes shaping cancer genome evolution over space and time. Multi-region and single-sample sequencing data was harnessed to temporally and clonally dissect mutations across 10 major cancer-types. The existence of branched tumour evolution and widespread heterogeneity was demonstrated. Although mutations in known cancer genes typically occurred early in cancer evolution, subclonal ‘actionable’ mutations, including BRAF (V600E), IDH1 (R132H), PIK3CA (E545K), and EGFR (L858R), were also identified. Temporal dissection of mutational signatures revealed that APOBEC-mediated mutagenesis is frequently a late event in cancer evolution and plays a key role in the acquisition of subclonal driver mutations. Copy number analysis suggested that genome doubling is prevalent across tumour types and that it frequently occurs early in tumour evolution in colorectal cancer. A cancer cell-line system was used to demonstrate that rare cells that survive genome-doubling display increased tolerance to chromosome aberrations and a genome-doubling event was found to be independently predictive of reduced relapse-free survival in two independent cohorts. Finally, the clinical impact of intra-tumour heterogeneity was explored in the context of cancer neo-antigens and immune-modulation. The number of clonal neoantigens was associated with survival outcome in lung adenocarcinoma patients and T cells reactive to clonal neo-antigens were identified. Sensitivity to anti-PD-1 therapy was dependent on neo-antigen clonal burden and intra-tumour heterogeneity. Thus, immunotherapeutic strategies targeting clonal neo-antigens in combination with checkpoint-blockade may provide a tractable approach to tackling lung adenocarcinomas. This thesis demonstrates how analyses of genomic data can shed light on the biology and clinical relevance of cancer evolution and intra-tumour heterogeneity.