Sleep-disordered breathing (SDB), encompassing both obstructive and central sleep apnea, is prevalent in at least 50% of stroke patients. Small studies have shown vast improvements in post-stroke functional recovery outcomes after the treatment of SDB by continuous positive airway pressure. However, compliance to this therapy is very poor in this complex patient group. There are alternative therapy options for SDB that may be more amenable for use in at least some post-stroke patients, including mandibular advancement, supine avoidance, and oxygen therapy. There are few studies, however, that demonstrate efficacy and compliance with these alternative therapies currently. Furthermore, novel SDB-phenotyping approaches may help to provide important clinical information to direct therapy selection in individual patients. Prior to realizing individualized therapy, we need a better understanding of the pathophysiology of SDB in post-stroke patients, including the role of inherent phenotypic traits, as well as the contribution of stroke size and location. This review summarizes the available literature on SDB pathophysiology and treatment in post-stroke patients, identifies gaps in the literature, and sets out areas for further research.