The association between Alzheimer's disease (AD) and sleep disturbances has received increasing scientific attention in the last decades. However, little is known about the impact of sleep and its disturbances on the development of preclinical AD stages, such as mild cognitive impairment. This review describes the evolution of knowledge about the potential bidirectional relationships between AD and sleep disturbances exploring recent large prospective studies and meta-analyses and studies of the possible mechanisms through which sleep and the neurodegenerative process could be associated. The review also makes a comprehensive exploration of the sleep characteristics of older people, ranging from cognitively normal individuals, through patients with mild cognitive impairment, up to the those with dementia with AD.