Children with Down syndrome (DS) are particularly prone to haematopoietic disorders. Paediatric myeloid malignancies in DS occur at an unusually high frequency and generally follow a well-defined stepwise clinical evolution. First, the acquisition of mutations in the GATA1 transcription factor gives rise to a transient myeloproliferative disorder (TMD) in DS newborns. While this condition spontaneously resolves in most cases, some clones can acquire additional mutations, which trigger myeloid leukaemia of Down syndrome (ML-DS). These secondary mutations are predominantly found in chromatin and epigenetic regulators—such as cohesin, CTCF or EZH2—and in signalling mediators of the JAK/STAT and RAS pathways. Most of them are also found in non-DS myeloid malignancies, albeit at extremely different frequencies. Intriguingly, mutations in proteins involved in the three-dimensional organization of the genome are found in nearly 50% of cases. How the resulting mutant proteins cooperate with trisomy 21 and mutant GATA1 to promote ML-DS is not fully understood. In this review, we summarize and discuss current knowledge about the sequential acquisition of genomic alterations in ML-DS.