Functional ankylosis of dental implants in alveolar bone is the current criterion to assess implant osseointegration from a biomechanical standpoint. In this literature review, the clinical significance and current available assessments of implant stability are discussed. However, these assessments demonstrate a variety of correlations to peri-implant structures and as such are difficult to translate to the clinical arena. Calculating the effective stiffness from homogenization of peri-implant tissues appears to be a more reliable approach to predict implant stability in preclinical studies, but the structure-biomechanical relationship remains a clinical challenge. Despite the limitations in functional assessments of dental implant stability and oral implant biomechanics, this review highlights some emerging approaches to adapt these measures to clinical situations.