Down syndrome (DS) is caused by trisomy of chromosome 21 (Hsa21) and is associated with a number of deleterious phenotypes, including learning disability, heart defects, early-onset Alzheimer's disease and childhood leukaemia. Individuals with DS are affected by these phenotypes to a variable extent; understanding the cause of this variation is a key challenge. Here, we review recent research progress in DS, both in patients and relevant animal models. In particular, we highlight exciting advances in therapy to improve cognitive function in people with DS and the significant developments in understanding the gene content of Hsa21. Moreover, we discuss future research directions in light of new technologies. In particular, the use of chromosome engineering to generate new trisomic mouse models and large-scale studies of genotype–phenotype relationships in patients are likely to significantly contribute to the future understanding of DS.