Acute myeloid leukaemia (AML) is an uncontrolled clonal proliferation of abnormal myeloid progenitor cells in the bone marrow and blood. Advances in cancer genomics have revealed the spectrum of somatic mutations that give rise to human AML and drawn our attention to its molecular evolution and clonal architecture. It is now evident that most AML genomes harbour small numbers of mutations, which are acquired in a stepwise manner. This characteristic, combined with our ability to identify mutations in individual leukaemic cells and our detailed understanding of normal human and murine haematopoiesis, makes AML an excellent model for understanding the principles of cancer evolution. Furthermore, a better understanding of how AML evolves can help us devise strategies to improve the therapy and prognosis of AML patients. Here, we draw from recent advances in genomics, clinical studies and experimental models to describe the current knowledge of the clonal evolution of AML and its implications for the biology and treatment of leukaemias and other cancers.