Balance and core stabilization exercises have often been associated with improved athlete performance and/or decreased incidence of injuries. While these exercises seem to be efficient in the prevention of injuries, there is insufficient evidence regarding their role in sport-specific performance and related functional movements. The aim of this scoping review is (1) to map the literature that investigates whether currently available variables of postural and core stability are functionally related to athlete performance in sports with high demands on body balance and spinal posture and (2) to identify gaps in the literature and suggest further research on this topic. The literature search conducted on MEDLINE, Scopus, Web of Science, PubMed, and Cochrane Library databases was completed by Google Scholar, SpringerLink, and Elsevier. Altogether 21 articles met the inclusion criteria. Findings revealed that postural stability plays an important role in performance in archery, biathlon, gymnastics, shooting, and team sports (e.g., basketball, hockey, soccer, tennis). Also core stability and strength represent an integral part of athlete performance in sports based on lifting tasks and trunk rotations. Variables of these abilities are associated with performance-related skills in cricket, cycling, running, and team sports (e.g., baseball, football, hockey, netball, soccer, tennis). Better neuromuscular control of postural and core stability contribute to more efficient functional movements specific to particular sports. Training programs incorporating general and sport-specific exercises that involve the use of postural and core muscles showed an improvement of body balance, back muscle strength, and endurance. However, there is controversy about whether the improvement in these abilities is translated into athletic performance. There is still a lack of research investigating the relationship of body balance and stability of the core with sport-specific performance. In particular, corresponding variables should be better specified in relation to functional movements in sports with high demands on postural and core stability. Identifying the relationship of passive, active, and neural mechanisms underlying balance control and spinal posture with athlete performance would provide a basis for a multifaced approach in designing training and testing tools addressing postural and core stability in athletes under sport-specific conditions.