Myeloid leukemia associated with Down syndrome (ML-DS) has a unique molecular landscape that differs from other subtypes of acute myeloid leukemia. ML-DS is often preceded by a myeloproliferative neoplastic condition called transient abnormal myelopoiesis (TAM) that disrupts megakaryocytic and erythroid differentiation. Over the last two decades, many genetic and epigenetic changes in TAM and ML-DS have been elucidated. These include overexpression of molecules and micro-RNAs located on chromosome 21, GATA1 mutations, and a range of other somatic mutations and chromosomal alterations. In this review, we summarize molecular changes reported in TAM and ML-DS and provide a comprehensive discussion of these findings. Recent advances in the development of CRISPR/Cas9-modified induced pluripotent stem cell-based disease models are also highlighted. However, despite significant progress in this area, we still do not fully understand the pathogenesis of ML-DS, and there are no targeted therapies. Initial diagnosis of ML-DS has a favorable prognosis, but refractory and relapsed disease can be difficult to treat; therapeutic options are limited in Down syndrome children by their stronger sensitivity to the toxic effects of chemotherapy. Because of the rarity of TAM and ML-DS, large-scale multi-center studies would be helpful to advance molecular characterization of these diseases at different stages of development and progression.