The configuration and control strategy of hybrid powertrain systems are significant for the development of hybrid electric vehicles (HEV) because they significantly affect their comprehensive performance. In this paper, the types, features, and applications of the mainstream hybrid powertrain configurations on the market in recent years are summarized and the effects of different configurations on the comprehensive performance of HEVs are compared. Moreover, the technical routes for each hybrid configuration are highlighted, as configuration optimization methods have become a technical difficulty. In addition, the technological advances in the steady-state energy management strategy and dynamic coordinated control strategy for hybrid powertrain systems are studied. The optimization of the steady-state energy management strategy mainly involves assigning the working point and working range of each power source reasonably. However, with the increase in the complexity of optimization algorithms, real-time control of HEVs still needs to be improved. The optimization of the dynamic coordinated control strategy mainly focuses on the stability and smoothness of the dynamic process involving switching and shifting the working mode. The optimization of the dynamic control process for the system remains to be further improved. It is pointed out that the configurations and strategies should be optimized jointly to obtain a comprehensive improvement in the system performance. This paper provides an informative basis and technical support for the design and optimization of a hybrid powertrain system.