Central sleep apnoea (CSA)—the temporary absence or diminution of ventilator effort during sleep—is seen in a variety of forms including periodic breathing in infancy and healthy adults at altitude and Cheyne-Stokes respiration in heart failure. In most circumstances, the cyclic absence of effort is paradoxically a consequence of hypersensitive ventilatory chemoreflex responses to oppose changes in airflow, i.e. elevated loop gain, leading to overshoot/undershoot ventilatory oscillations. Considerable evidence illustrates overlap between CSA and obstructive sleep apnoea (OSA), including elevated loop gain in patients with OSA and the presence of pharyngeal narrowing during central apnoeas. Indeed, treatment of OSA, whether via CPAP, tracheostomy, or oral appliances, can reveal CSA, an occurrence referred to as complex sleep apnoea. Factors influencing loop gain include increased chemosensitivity (increased controller gain), reduced damping of blood gas levels (increased plant gain) and increased lung to chemoreceptor circulatory delay. Sleep-wake transitions and pharyngeal dilator muscle responses effectively raise the controller gain and therefore also contribute to total loop gain and overall instability. In some circumstances, for example apnoea of infancy and central congenital hypoventilation syndrome, central apnoeas are the consequence of ventilatory depression and defective ventilatory responses, i.e. low loop gain. The efficacy of available treatments for CSA can be explained in terms of their effects on loop gain, e.g. CPAP improves lung volume (plant gain), stimulants reduce the alveolar-inspired PCO2 difference, supplemental oxygen lowers chemosensitivity. Understanding the magnitude of loop gain and the mechanisms contributing to instability may facilitate personalised interventions for CSA.