Actuators play a crucial role in robotics, determining the force and speed capabilities necessary for varied tasks, directly affecting the performance of the robotic system. With the growing reliance on robotics in both industrial applications and daily life, innovative actuator research has expanded significantly. Despite advances, traditional actuators encounter limitations in performance and operational range due to inherent physical constraints. To address these challenges, variable transmission mechanisms (VTMs) have emerged over the past decade as one of the alternative solutions, enhancing the adaptability and efficiency of robotic systems. However, there is currently a lack of survey articles that comprehensively cover the mechanisms and working principles of VTMs in robotics. This review article fills this gap by offering an extensive analysis of VTM applications in robotics. It categorizes VTMs based on their mechanisms and principles, presents case studies on both commercial and experimental VTMs, and provides insights into future prospects.