Haematopoiesis is governed by haematopoietic stem cells (HSCs) that produce all lineages of blood and immune cells. The maintenance of blood homeostasis requires a dynamic response of HSCs to stress, and dysregulation of these adaptive-response mechanisms underlies the development of myeloid leukaemia. Leukaemogenesis often occurs in a stepwise manner, with genetic and epigenetic changes accumulating in pre-leukaemic HSCs prior to the emergence of leukaemic stem cells (LSCs) and the development of acute myeloid leukaemia. Clinical data have revealed the existence of age-related clonal haematopoiesis, or the asymptomatic clonal expansion of mutated blood cells in the elderly, and this phenomenon is connected to susceptibility to leukaemic transformation. Here we describe how selection for specific mutations that increase HSC competitive fitness, in conjunction with additional endogenous and environmental changes, drives leukaemic transformation. We review the ways in which LSCs take advantage of normal HSC properties to promote survival and expansion, thus underlying disease recurrence and resistance to conventional therapies, and we detail our current understanding of leukaemic 'stemness' regulation. Overall, we link the cellular and molecular mechanisms regulating HSC behaviour with the functional dysregulation of these mechanisms in myeloid leukaemia and discuss opportunities for targeting LSC-specific mechanisms for the prevention or cure of malignant diseases.