Adult obstructive sleep apnoea (OSA) is associated with cognitive dysfunction. While many review articles have attempted to summarize the evidence for this association, it remains difficult to determine which domains of cognition are affected by OSA. This is because of marked differences in the nature of these reviews (e.g. many are unsystematic) and the many different tasks and domains assessed. This paper addresses this issue by comparing the results of only systematic reviews or meta-analyses assessing the effects of OSA on cognition, the relationship between OSA severity and cognition, and/or the effects of treatment on cognition in OSA. Electronic databases and hand-searching were undertaken to select reviews that reported on these areas. We found 33 reviews; five reviews met predetermined, stringent selection criteria. The majority of reviews supported deficits in attention/vigilance, delayed long-term visual and verbal memory, visuospatial/constructional abilities, and executive function in individuals with OSA. There is also general agreement that language ability and psychomotor function are unaffected by OSA. Data are equivocal for the effects of OSA on working memory, short-term memory and global cognitive functioning. Attention/vigilance dysfunction appears to be associated with sleep fragmentation and global cognitive function with hypoxaemia. Continuous positive airway pressure treatment of OSA appears to improve executive dysfunction, delayed long-term verbal and visual memory, attention/vigilance and global cognitive functioning. In order to improve our understanding of cognitive dysfunction in OSA, future research should pay particular attention to participant characteristics, measures of disease severity and choice of neuropsychological tests.