Obstructive sleep apnea (OSA) is a nocturnal breathing disorder that is associated with cognitive impairment. The primary determinants of cognitive deficits in OSA are thought to be sleep disruption and blood gas abnormalities. Cognitive impairment is also seen in other disorders that are characterised primarily by sleep disturbance (e.g., sleep restriction/deprivation, insomnia) or hypoxia/hypercarbia (e.g., chronic obstructive pulmonary disease (COPD)). Assessment of the cognitive deficits observed in these other disorders could help better define the mechanisms underlying cognitive deficits in OSA. This study utilised meta-review methodology to examine the findings from systematic reviews and meta-analyses of the effects of untreated OSA, COPD, insomnia, and sleep deprivation on cognitive function in adults, compared with norms or controls. Eighteen papers met inclusion criteria: seven in OSA, two in insomnia, five in COPD, and four in sleep deprivation. OSA and COPD were both accompanied by deficits in attention, memory, executive function, psychomotor function, and language abilities, suggesting that hypoxia/hypercarbia may be an important determinant of deficits in these domains in OSA. Both OSA and sleep deprivation studies were accompanied by deficits in attention and memory, suggesting that short-term sleep disturbance in OSA may contribute to deficits in these domains. Visuospatial deficits were unique to OSA, suggesting the contribution of a mechanism other than sleep disturbance and hypoxia/hypercarbia to this problem. Our findings suggest that the cognitive deficits associated with untreated OSA are multidimensional, with different physiological disturbances responsible for differing cognitive problems.