Clonal haematopoiesis (CH) is a common, age-related expansion of blood cells with somatic mutations that is associated with an increased risk of haematological malignancies, cardiovascular disease and all-cause mortality. CH may be caused by point mutations in genes associated with myeloid neoplasms, chromosomal copy number changes and loss of heterozygosity events. How inherited and environmental factors shape the incidence of CH is incompletely understood. Even though the several varieties of CH may have distinct phenotypic consequences, recent research points to an underlying genetic architecture that is highly overlapping. Moreover, there are numerous commonalities between the inherited variation associated with CH and that which has been linked to age-associated biomarkers and diseases. In this Review, we synthesize what is currently known about how inherited variation shapes the risk of CH and how this genetic architecture intersects with the biology of diseases that occur with ageing.