Reverse total shoulder arthroplasty (RTSA) is an established treatment for elderly patients with irreparable rotator cuff tears, complex proximal humerus fractures, and revision arthroplasty; however, with the increasing indications for RTSA over the last decade and younger implant recipients, post-operative complications have become more frequent, which has driven advances in computational modeling and simulation of reverse shoulder biomechanics. The objective of this study was to provide a review of previously published studies that employed computational modeling to investigate complications associated with RTSA. Models and applications were reviewed and categorized into four possible complications that included scapular notching, component loosening, glenohumeral joint instability, and acromial and scapular spine fracture, all of which remain a common cause of significant functional impairment and revision surgery. The computational shoulder modeling studies reviewed were primarily used to investigate the effects of implant design, intraoperative component placement, and surgical technique on postoperative shoulder biomechanics after RTSA, with the findings ultimately used to elucidate and mitigate complications. The most significant challenge associated with the development of computational models is in the encapsulation of patient-specific anatomy and surgical planning. The findings of this review provide a basis for future direction in computational modeling of the reverse shoulder.