Cellular behaviors such as migration, spreading, and differentiation arise from the interplay of cell-matrix interactions. The comprehension of this interplay has been advanced by the motor-clutch model, a theoretical framework that captures the binding-unbinding kinetics of mechanosensitive membrane-bound proteins involved in mechanochemical signaling, such as integrins. Since its introduction and subsequent development as a computational tool, the motor clutch model has been instrumental in elucidating the impact of biophysical factors on cellular mechanobiology. This review aims to provide a comprehensive overview of recent advances in the motor-clutch modeling framework, its role in elucidating the relationships between mechanical forces and cellular processes, and its potential applications in mechanomedicine.