The complexity of central breathing disturbances during sleep has become increasingly obvious. They present as central sleep apnoeas (CSAs) and hypopnoeas, periodic breathing with apnoeas, or irregular breathing in patients with cardiovascular, other internal or neurological disorders, and can emerge under positive airway pressure treatment or opioid use, or at high altitude. As yet, there is insufficient knowledge on the clinical features, pathophysiological background and consecutive algorithms for stepped-care treatment. Most recently, it has been discussed intensively if CSA in heart failure is a “marker” of disease severity or a “mediator” of disease progression, and if and which type of positive airway pressure therapy is indicated. In addition, disturbances of respiratory drive or the translation of central impulses may result in hypoventilation, associated with cerebral or neuromuscular diseases, or severe diseases of lung or thorax. These statements report the results of an European Respiratory Society Task Force addressing actual diagnostic and therapeutic standards. The statements are based on a systematic review of the literature and a systematic two-step decision process. Although the Task Force does not make recommendations, it describes its current practice of treatment of CSA in heart failure and hypoventilation.