Most patients with heart failure (HF) have sleep-disordered breathing (SDB), with central (rather than obstructive) sleep apnea becoming the predominant form in patients with more severe disease. Cyclical apnea and hypopneas are associated with sleep disturbance, hypoxemia, hemodynamic changes, and sympathetic activation. These patients have a worse prognosis than those without SDB. Mask-based therapies of positive airway pressure targeted at SDB can improve measures of sleep quality and can partially normalize the sleep and respiratory physiology. However, recent randomized trials of cardiovascular outcomes in central sleep apnea in chronic HF with reduced ejection fraction have had neutral findings or suggested the possibility of harm, likely from an increased rate of sudden death. Further randomized outcome studies are required to determine whether mask-based treatment is appropriate for patients with chronic HF with reduced ejection fraction and obstructive sleep apnea, for patients with heart failure with preserved ejection fraction, and for patients with decompensated heart failure. New therapies for sleep apnea (e.g., implantable phrenic nerve stimulators) also require robust assessment. No longer can the surrogate endpoints of improvement in respiratory and sleep metrics be taken as adequate therapeutic outcome measures in patients with HF and sleep apnea.