Here we review the impact of obstructive sleep apnea (OSA) on biomarkers of Alzheimer's disease (AD) pathogenesis, neuroanatomy, cognition and neurophysiology, and present the research investigating the effects of continuous positive airway pressure (CPAP) therapy. OSA is associated with an increase in AD markers amyloid-β and tau measured in cerebrospinal fluid (CSF), by Positron Emission Tomography (PET) and in blood serum. There is some evidence suggesting CPAP therapy normalizes AD biomarkers in CSF but since mechanisms for amyloid-β and tau production/clearance in humans are not completely understood, these findings remain preliminary. Deficits in the cognitive domains of attention, vigilance, memory and executive functioning are observed in OSA patients with the magnitude of impairment appearing stronger in younger people from clinical settings than in older community samples. Cognition improves with varying degrees after CPAP use, with the greatest effect seen for attention in middle age adults with more severe OSA and sleepiness. Paradigms in which encoding and retrieval of information are separated by periods of sleep with or without OSA have been done only rarely, but perhaps offer a better chance to understand cognitive effects of OSA than isolated daytime testing. In cognitively normal individuals, changes in EEG microstructure during sleep, particularly slow oscillations and spindles, are associated with biomarkers of AD, and measures of cognition and memory. Similar changes in EEG activity are reported in AD and OSA, such as “EEG slowing” during wake and REM sleep, and a degradation of NREM EEG microstructure. There is evidence that CPAP therapy partially reverses these changes but large longitudinal studies demonstrating this are lacking. A diagnostic definition of OSA relying solely on the Apnea Hypopnea Index (AHI) does not assist in understanding the high degree of inter-individual variation in daytime impairments related to OSA or response to CPAP therapy. We conclude by discussing conceptual challenges to a clinical trial of OSA treatment for AD prevention, including inclusion criteria for age, OSA severity, and associated symptoms, the need for a potentially long trial, defining relevant primary outcomes, and which treatments to target to optimize treatment adherence.