Obstructive sleep apnoea is a challenging medical problem due to its prevalence, its impact on quality of life and performance in school and professionally, the implications for risk of accidents, and comorbidities and mortality. Current research has carved out a broad spectrum of clinical phenotypes and defined major pathophysiological components. These findings point to the concept of personalised therapy, oriented on both the distinct clinical presentation and the most relevant pathophysiology in the individual patient. This leads to questions of whether sufficient therapeutic options other than positive airway pressure (PAP) alone are available, for which patients they may be useful, if there are specific indications for single or combined treatment, and whether there is solid scientific evidence for recommendations. This review describes our knowledge on PAP and non-PAP therapies to address upper airway collapsibility, muscle responsiveness, arousability and respiratory drive. The spectrum is broad and heterogeneous, including technical and pharmaceutical options already in clinical use or at an advanced experimental stage. Although there is an obvious need for more research on single or combined therapies, the available data demonstrate the variety of effective options, which should replace the unidirectional focus on PAP therapy.