Next-generation deep genome sequencing has only recently allowed us to quantitatively dissect the extent of heterogeneity within a tumour, resolving patterns of cancer evolution. Intratumour heterogeneity and natural selection contribute to resistance to anticancer therapies in the advanced setting. Recent evidence has also revealed that cancer evolution might be constrained. In this review, we discuss the origins of intratumour heterogeneity and subsequently focus on constraints imposed upon cancer evolution. The presence of (1) parallel evolution, (2) convergent evolution and (3) the biological impact of acquiring mutations in specific orders suggest that cancer evolution may be exploitable. These constraints on cancer evolution may help us identify cancer evolutionary rule books, which could eventually inform both diagnostic and therapeutic approaches to improve survival outcomes.