Major international projects are underway that are aimed at creating a comprehensive catalogue of all the genes responsible for the initiation and progression of cancer. These studies involve the sequencing of matched tumour-normal samples followed by mathematical analysis to identify those genes in which mutations occur more frequently than expected by random chance. Here we describe a fundamental problem with cancer genome studies: as the sample size increases, the list of putatively significant genes produced by current analytical methods burgeons into the hundreds. The list includes many implausible genes (such as those encoding olfactory receptors and the muscle protein titin), suggesting extensive false-positive findings that overshadow true driver events. We show that this problem stems largely from mutational heterogeneity and provide a novel analytical methodology, MutSigCV, for resolving the problem. We apply MutSigCV to exome sequences from 3,083 tumour-normal pairs and discover extraordinary variation in mutation frequency and spectrum within cancer types, which sheds light on mutational processes and disease aetiology, and in mutation frequency across the genome, which is strongly correlated with DNA replication timing and also with transcriptional activity. By incorporating mutational heterogeneity into the analyses, MutSigCV is able to eliminate most of the apparent artefactual findings and enable the identification of genes truly associated with cancer.