There are various hybrid powertrain architectures which are in use. The general goals of a hybrid transmission design are to realize the different operating modes of a hybrid vehicle system, such as the capability to run motor-alone mode, engine-alone mode, combined mode, power split mode, regenerative braking mode, and stationary charging operations. In addition, it is important to be able to control engine power and speed during hybrid operations so that better fuel economy and lower emissions can be achieved for all ranges of vehicle speeds and power demands. Lastly, the system design should be easy to implement and control, and bear low overall cost. This chapter discusses the principles of a few advanced hybrid electric powertrain architectures. These architectures include the popular GM two-mode hybrid and its variations, dual-clutch-based hybrid, Tsai's hybrid, Zhang's hybrid, Renault hybrid, and Timken hybrid.The steady state operating modes and torque/speed relationships are presented first. Then, the HEV powertrain dynamics will be briefly discussed for the Toyota hybrid transmission.Hybrid Electric Vehicles: Principles and Applications with Practical Perspectives, First Edition.