Sleep in chronic obstructive pulmonary disease (COPD) is commonly associated with oxygen desaturation, which may exceed the degree of desaturation during maximum exercise, both subjectively and objectively impairing sleep quality. The mechanisms of desaturation include hypoventilation and ventilation to perfusion mismatching. The consequences of this desaturation include cardiac arrhythmias, pulmonary hypertension and nocturnal death, especially during acute exacerbations. Coexistence of COPD and obstructive sleep apnoea (OSA), referred to as overlap syndrome, has been estimated to occur in 1% of the general adult population. Overlap patients have worse sleep-related hypoxaemia and hypercapnia than patients with COPD or OSA alone. OSA has a similar prevalence in COPD as in a general population of similar age, but oxygen desaturation during sleep is more pronounced when the two conditions coexist. Management of sleep-related problems in COPD should particularly focus on minimising sleep disturbance via measures to limit cough and dyspnoea; nocturnal oxygen therapy is not generally indicated for isolated nocturnal hypoxaemia. Treatment with continuous positive airway pressure alleviates hypoxaemia, reduces hospitalisation and pulmonary hypertension, and improves survival.