Children with Down syndrome (DS) have a marked increase in susceptibility to Acute Megakaryoblastic Leukaemia (DS‐AMKL) and the closely linked neonatal preleukaemic syndrome, Transient Myeloproliferative Disorder (DS‐TMD). The distinct stages of DS‐TMD and DS‐AMKL provide an excellent tractable model to study leukaemogenesis. This review focuses on recent studies describing clinical, haematological and biological features of DS‐AMKL and DS‐TMD. The findings from these studies suggest that mutations in the key haemopoietic regulator GATA1 (GATA binding protein 1) in DS‐AMKL and DS‐TMD may be useful in diagnosis and assessing minimal residual disease. These findings raise the possibility of population‐based screening strategies for DS‐TMD and the development of treatment to eliminate the preleukaemic TMD clone to prevent DS‐AMKL. Advances in our understanding of perturbed haemopoiesis in DS, the role of GATA1 and of cooperating mutations are also discussed. These findings have implications for leukaemia biology more broadly given the frequency of acquired trisomy in other human leukaemias.