Accumulating evidence suggests that many classes of DNA repeats exhibit attributes that distinguish them from other genetic variants, including the fact that they are more liable to mutation; this enables them to mediate genetic plasticity. The expansion of tandem repeats, particularly of short tandem repeats, can cause a range of disorders (including Huntington disease, various ataxias, motor neuron disease, frontotemporal dementia, fragile X syndrome and other neurological disorders), and emerging data suggest that tandem repeat polymorphisms (TRPs) can also regulate gene expression in healthy individuals. TRPs in human genomes may also contribute to the missing heritability of polygenic disorders. A better understanding of tandem repeats and their associated repeatome, as well as their capacity for genetic plasticity via both germline and somatic mutations, is needed to transform our understanding of the role of TRPs in health and disease.