While this study is on the clinical development of temporomandibular joint disorders and understanding various biomechanical approaches through finite element analysis as a panacea, the primary aim is to perform a literature review. Usage of the biomedical prosthesis, over the years, including the initial development and later modernization with image processing and computer simulations, are briefly discussed from 1800 to 2021. Manual data handling was used to select 503 journal papers, of which 116 were further studied in this review. This review explains the complete biomechanical structure of the temporomandibular joint (TMJ), as it disclosed possible reasons for the disorders and shortcomings in the medical treatments. In the Boundary Condition and Discussion sections, the paper discussed the boundary conditions and the results of various studies from 2000 to 2021. It also discussed 36 papers with temporomandibular joint replacement (TMJR) devices, providing important information on the stress–strain distributions in the implant and the mandible-fossa component. Both custom and stock devices are discussed with a finite element method (FEM) approach, with a proper evaluation of multiple software for individual studies. Finally, TMJR devices are considered helpful for treating TMJ disorders. The FEM approach should be considered a precise and valuable biomechanical simulation tool for modifying and improving next-generation prosthetic devices.