There is growing clinical evidence showing the impact of sleep disturbance on the development of Alzheimer’s disease (AD). It has been proposed that intermittent hypoxia and sleep fragmentation, which are hallmarks of obstructive sleep apnoea hypopnoea syndrome (OSAHS), are physiological changes that may contribute to cognitive impairment. Sleep fragmentation reduces slow-wave sleep duration affecting the efficiency of the brain clearance system, allowing metabolic proteins to accumulate. These proteins contribute to neurodegeneration, brain atrophy, and cognitive impairment. Improvements in fluid diffusion which leads to the reduction in the accumulation of metabolic proteins, have been observed after positive airway pressure (PAP) treatment. Treating OSAHS may be effective in reducing the risk of neuronal damage and improve cognitive function. This review outlines the current knowledge associating OSAHS and AD and discusses the effect of PAP treatment on cognitive function, AD biomarkers, and the brain clearance system.