The aim of this review was to summarize the existing literature on the association between sleep problems and cognition, function, and behavior in children with Down syndrome. Methods: Embase, PubMed, CINAHL, and PsychINFO databases were searched to retrieve all studies published between 1990 and 2018 that evaluated the relationship between sleep and cognition, function, or behavior in children with Down syndrome. Results: Fifteen articles were included, which were mostly of a cohort or case-controlled design. Five articles addressed sleep and cognition only, 6 reported on sleep and behavior, and only 1 reported on sleep and functional ability. Three papers evaluated sleep and both cognition and behavior. Findings varied across studies with methodological differences, making it difficult to directly compare results. The association between sleep and behavior or cognition in children with Down syndrome remains uncertain, but a large study in 110 children provides strong evidence of a negative impact of sleep disorders on the accomplishment of daily life habits. Conclusions: The impact of coexisting sleep disorders in children with Down syndrome has not been widely studied, with only 15 relevant studies found through an extensive literature review. Large well-designed studies are required to fully understand this relationship further. This is important as sleep-disordered breathing and difficulties with sleep patterns and routines are highly prevalent in children with Down syndrome. Sleep may be one of the few treatable factors that can assist in improving long-term outcomes in this population.