The expansion of repeated sequences is the cause of over 30 inherited genetic diseases, including Huntington disease, myotonic dystrophy (types 1 and 2), fragile X syndrome, many spinocerebellar ataxias, and some cases of amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). Repeat expansions are dynamic, and disease inheritance and progression are influenced by the size and the rate of expansion. Thus, an understanding of the various cellular mechanisms that cooperate to control or promote repeat expansions is of interest to human health. In addition, the study of repeat expansion and contraction mechanisms has provided insight into how repair pathways operate in the context of structure-forming DNA, as well as insights into non-canonical roles for repair proteins. Here we review the mechanisms of repeat instability, with a special emphasis on the knowledge gained from the various model systems that have been developed to study this topic. We cover the repair pathways and proteins that operate to maintain genome stability, or in some cases cause instability, and the cross-talk and interactions between them.