At fifteen different genomic locations, the expansion of a CAG/CTG repeat causes a neurodegenerative or neuromuscular disease, the most common being Huntington’s disease and myotonic dystrophy type 1. These disorders are characterized by germline and somatic instability of the causative CAG/CTG repeat mutations. Repeat lengthening, or expansion, in the germline leads to an earlier age of onset or more severe symptoms in the next generation. In somatic cells, repeat expansion is thought to precipitate the rate of disease. The mechanisms underlying repeat instability are not well understood. Here we review the mammalian model systems that have been used to study CAG/CTG repeat instability, and the modifiers identified in these systems. Mouse models have demonstrated prominent roles for proteins in the mismatch repair pathway as critical drivers of CAG/CTG instability, which is also suggested by recent genome-wide association studies in humans. We draw attention to a network of connections between modifiers identified across several systems that might indicate pathway crosstalk in the context of repeat instability, and which could provide hypotheses for further validation or discovery. Overall, the data indicate that repeat dynamics might be modulated by altering the levels of DNA metabolic proteins, their regulation, their interaction with chromatin, or by direct perturbation of the repeat tract. Applying novel methodologies and technologies to this exciting area of research will be needed to gain deeper mechanistic insight that can be harnessed for therapies aimed at preventing repeat expansion or promoting repeat contraction.