The ubiquitin–proteasome system (UPS) plays a critical role in removing unwanted intracellular proteins and is involved in protein quality control, signalling and cell death. Because the heart is subject to continuous metabolic and mechanical stress, the proteasome plays a particularly important role in the heart, and proteasome dysfunction has been suggested as a causative factor in cardiac dysfunction. Proteasome impairment has been detected in cardiomyopathies, heart failure, myocardial ischaemia, and hypertrophy. Proteasome inhibition is also sufficient to cause cardiac dysfunction in healthy pigs, and patients using a proteasome inhibitor for cancer therapy have a higher incidence of heart failure. In this Topical Review we discuss the experimental data which suggest UPS dysfunction is a common feature of cardiomyopathies, with an emphasis on hypertrophic cardiomyopathy caused by sarcomeric mutations. We also propose potential mechanisms by which cardiomyopathy‐causing mutations may lead to proteasome impairment, such as altered calcium handling and increased oxidative stress due to mitochondrial dysfunction.