The majority of patients with heart failure have sleep-disordered breathing. There are two major types—obstructive (where the upper airway collapses, but respiratory effort continues) and central (with loss of central respiratory drive). The cyclical apnoea and hypopneas are associated with sleep disturbance, hypoxaemia, haemodynamic changes, and sympathetic activation. Heart failure patients appear to be partially protected from the daytime somnolence that usually accompanies sleep-disordered breathing, perhaps by a high level of background sympathetic activation. Patients with sleep-disordered breathing have a worse prognosis than those without. Improving the control of the heart failure syndrome can improve sleep-disordered breathing. Mask-based therapies of positive airway pressure targeted at sleep-disordered breathing can improve measures of sleep quality and partially normalize the sleep and respiratory physiology, but recent randomized trials of cardiovascular outcomes in central sleep apnoea have been neutral or have even suggested the possibility of harm, likely from increased sudden death. Further randomized outcome studies are required to determine whether mask-based treatment is appropriate for patients with chronic systolic heart failure and obstructive sleep apnoea, for those with heart failure with preserved ejection fraction, and for those with decompensated heart failure. New therapies for central sleep apnoea—such as implantable phrenic nerve stimulators—also require robust assessment.