The goal of this review article is to summarize our knowledge and understanding of the overlapping (interdisciplinary) areas of senescence, sleep, and circadian rhythms. Our overview comprehensively (and visually wherever possible), emphasizes the organizational, dynamic, and plastic nature of both sleep and circadian timing system (CTS) during senescent processes in animals and in humans. In this review, we focus on the studies that deal with sleep and circadian rhythms in aged animals and how these studies have closely correlated to and advanced our understanding of similar processes in ageing humans. Our comprehensive summary of various aspects of the existing research on animal and human ageing, both normal and pathological, presented in this review underscores the invaluable advantage of close collaboration between clinicians and basic research scientists and the future challenges inherent in this collaboration. First, our review addresses the common age-related changes that occur in sleep and temporal organization of both animals and humans. Second, we examine the specific modifications that often accompany sleep and CTS during aging. Third, we discuss the clinical epidemiology of sleep dysfunctions during ageing and their current clinical management, both pharmacological and non-pharmacological. Finally, we predict the possible future promises for complementary and alternative medicine (CAM) that pave the way to the emergence of a "Holistic Sleep Medicine" approach to the treatment of sleep disorders in the ageing population. Further studies will provide additional valuable insights into the understanding of both sleep and circadian rhythms during senescence.