This review focuses on two phenomena that are initiated during and after exposure to intermittent hypoxia. The two phenomena are referred to as long‐term facilitation and progressive augmentation of respiratory motor output. Both phenomena are forms of respiratory plasticity. Long‐term facilitation is characterized by a sustained elevation in respiratory activity after exposure to intermittent hypoxia. Progressive augmentation is characterized by a gradual increase in respiratory activity from the initial to the final hypoxic exposure. There is much speculation that long‐term facilitation may have a significant role in individuals with sleep apnoea because this disorder is characterized by periods of upper airway collapse accompanied by intermittent hypoxia, one stimulus known to induce long‐term facilitation. It has been suggested that activation of long‐term facilitation may serve to mitigate apnoea by facilitating ventilation and, more importantly, upper airway muscle activity. We examine the less discussed but equally plausible situation that exposure to intermittent hypoxia might ultimately lead to the promotion of apnoea. There are at least two scenarios in which apnoea might be promoted following exposure to intermittent hypoxia. In both scenarios, long‐term facilitation of upper airway muscle activity is initiated but ultimately rendered ineffective because of other physiological conditions. Thus, one of the primary goals of this review is to discuss, with support from basic and clinical studies, whether various forms of respiratory motor neuronal plasticity have a beneficial and/or a detrimental impact on breathing stability in individuals with sleep apnoea.