Tendon-sheath actuation mechanism has been adopted in many robotic applications as it can provide a simple and dexterous remote transmission mode. However, inherent nonlinearities such as backlash and hysteresis arise due to sheath-tendon friction. These nonlinear characteristics, influenced by tendon-sheath configurations, significantly degrade transmission efficiency and control performance, posing challenges in applications demanding high control accuracy. Therefore, establishing accurate transmission characteristic models for tendon-sheath systems is crucial for their robotic applications. This chapter introduce the force and displacement transmission modeling methods of the tendon-sheath systems, including static models and dynamic models. Both the single tendon-sheath transmission mechanism and the double tendon-sheath transmission mechanism are discussed, and the model performance are analyzed by simulation and experiments. The transmission models introduced in this chapter can be applied to the practical applications of the tendon-sheath system to describe the system output, evaluate the transmission capability, and develop precise motion control algorithms, etc.