Biomechanical studies play an important role in understanding the pathophysiology of sleep disorders and providing insights to maintain sleep health. Computational methods facilitate a versatile platform to analyze various biomechanical factors in silico, which would otherwise be difficult through in vivo experiments. The objective of this review is to examine and map the applications of computational biomechanics to sleep-related research topics, including sleep medicine and sleep ergonomics. A systematic search was conducted on PubMed, Scopus, and Web of Science. Research gaps were identified through data synthesis on variants, outcomes, and highlighted features, as well as evidence maps on basic modeling considerations and modeling components of the eligible studies. Twenty-seven studies (n = 27) were categorized into sleep ergonomics (n = 2 on pillow; n = 3 on mattress), sleep-related breathing disorders (n = 19 on obstructive sleep apnea), and sleep-related movement disorders (n = 3 on sleep bruxism). The effects of pillow height and mattress stiffness on spinal curvature were explored. Stress on the temporomandibular joint, and therefore its disorder, was the primary focus of investigations on sleep bruxism. Using finite element morphometry and fluid-structure interaction, studies on obstructive sleep apnea investigated the effects of anatomical variations, muscle activation of the tongue and soft palate, and gravitational direction on the collapse and blockade of the upper airway, in addition to the airflow pressure distribution. Model validation has been one of the greatest hurdles, while single-subject design and surrogate techniques have led to concerns about external validity. Future research might endeavor to reconstruct patient-specific models with patient-specific loading profiles in a larger cohort. Studies on sleep ergonomics research may pave the way for determining ideal spine curvature, in addition to simulating side-lying sleep postures. Sleep bruxism studies may analyze the accumulated dental damage and wear. Research on OSA treatments using computational approaches warrants further investigation.