Myotonic dystrophies (DM), the most common muscular dystrophies, are known to have significant sleep disturbances. We analyzed the literature on sleep and excessive daytime sleepiness (EDS) in DM over the past 30 years. In this review we provide a brief overview of sleep, sleep disorders, and methods of assessment. We also analyze data regarding major sleep disorders in DM patients, including: sleep‐disordered breathing (SDB), with both central and obstructive sleep apneas (CSA,OSA); EDS; sleep‐related movement disorders; and poor sleep quality. We review the possible pathogenesis of these disorders and outline management strategies. We also consider possible future avenues for research. The findings highlight the complex set of sleep‐related problems, including the primary abnormality of sleep control in myotonic dystrophies. In individual patients the roles of poor sleep hygiene, SDB, primary hypersomnia, and excess fatigue require careful assessment for appropriate management.