Excessive daytime sleepiness (EDS) is a major symptom of obstructive sleep apnoea (OSA), defined as the inability to stay awake during the day. Its clinical descriptors remain elusive, and the pathogenesis is complex, with disorders such as insufficient sleep and depression commonly associated. Subjective EDS can be evaluated using the Epworth Sleepiness Scale, in which the patient reports the probability of dozing in certain situations; however, its reliability has been challenged. Objective tests such as the multiple sleep latency test or the maintenance of wakefulness test are not commonly used in patients with OSA, since they require nocturnal polysomnography, daytime testing and are expensive. Drugs for EDS are available in the United States but were discontinued in Europe some time ago. For European respiratory physicians, treatment of EDS with medication is new and they may lack experience in pharmacological treatment of EDS, while novel wake-promoting drugs have been recently developed and approved for clinical use in OSA patients in the USA and Europe. This review will discuss 1) the potential prognostic significance of EDS in OSA patients at diagnosis, 2) the prevalence and predictors of residual EDS in treated OSA patients, and 3) the evolution of therapy for EDS specifically for Europe.