Individuals with Down syndrome are genetically predisposed to developing acute megakaryoblastic leukemia. This myeloid leukemia associated with Down syndrome (ML–DS) demonstrates a model of step-wise leukemogenesis with perturbed hematopoiesis already presenting in utero, facilitating the acquisition of additional driver mutations such as truncating GATA1 variants, which are pathognomonic to the disease. Consequently, the affected individuals suffer from a transient abnormal myelopoiesis (TAM)—a pre-leukemic state preceding the progression to ML–DS. In our review, we focus on the molecular mechanisms of the different steps of clonal evolution in Down syndrome leukemogenesis, and aim to provide a comprehensive view on the complex interplay between gene dosage imbalances, GATA1 mutations and somatic mutations affecting JAK-STAT signaling, the cohesin complex and epigenetic regulators.