Sleep disorders are common in patients with Alzheimer’s disease, and can even occur in patients with amnestic mild cognitive impairment, which appears before Alzheimer’s disease. Sleep disorders further impair cognitive function and accelerate the accumulation of amyloid-β and tau in patients with Alzheimer’s disease. At present, sleep disorders are considered as a risk factor for, and may be a predictor of, Alzheimer’s disease development. Given that sleep disorders are encountered in other types of dementia and psychiatric conditions, sleep-related biomarkers to predict Alzheimer’s disease need to have high specificity and sensitivity. Here, we summarize the major Alzheimer’s disease-specific sleep changes, including abnormal non-rapid eye movement sleep, sleep fragmentation, and sleep-disordered breathing, and describe their ability to predict the onset of Alzheimer’s disease at its earliest stages. Understanding the mechanisms underlying these sleep changes is also crucial if we are to clarify the role of sleep in Alzheimer’s disease. This paper therefore explores some potential mechanisms that may contribute to sleep disorders, including dysregulation of the orexinergic, glutamatergic, and γ-aminobutyric acid systems and the circadian rhythm, together with amyloid-β accumulation. This review could provide a theoretical basis for the development of drugs to treat Alzheimer’s disease based on sleep disorders in future work.