Tumours accumulate many somatic mutations in their lifetime. Some of these mutations, drivers, convey a selective advantage and can induce clonal expansions. Incomplete clonal expansions give rise to intra-tumour heterogeneity. Somatic mutations can be measured through massively parallel sequencing, where mutations that are supporting incomplete expansions will appear as subclonal. These mutations can be used as a marker of the existence of the expansion and allow for a window into the clonal and subclonal architecture of the tumour at diagnosis. During my Ph.D. I have developed computational methods to infer intra-tumour hetero- geneity from massively parallel sequencing data and applied these to the 2,778 tumour whole genome sequences in the International Cancer Genome Consortium Pan-Cancer Analysis of Whole Genomes initiative to paint the pan-cancer landscape of intra-tumour heterogeneity. I will first introduce the methods; a method to call somatic copy number alterations (Battenberg) and a method to infer subclones from single nucleotide variants (DPClust). Both are extensively validated on simulated and on real data, and I describe a rigorous quality control procedure. The methods are then applied to a single sample to showcase what can be learned about the life history of a cancer, before introducing additional computational methods for a pan-cancer study of heterogeneity. Finally, I describe the findings. I find that nearly all cancers, for which there is sufficient power, contain at least one subclone (96.7% of 1,801 primary tumours). The subclones contain driver mutations that are under positive selection, and known cancer genes contain subclonal driver mutations in low proportions. 9.5% of tumours contain only subclonal drivers that are clinically actionable, suggesting that heterogeneity could inform treatment choices. Finally, the analysis reveals that activity of smoking and UV-light associated mutational signatures goes down as the tumour evolves, while activity of the APOBEC associated signatures goes up.