The turbine hybrid electric propulsion system is an important form of green aviation. Unlike the single form of aviation power scheme, the hybrid energy system is flexible in architecture, uses two or more energy forms, and has diverse energy sources. Under different mission requirements, it needs to meet the requirements of mass balance, energy balance, and power demand, etc. Therefore, The control and distribution management between different energy systems have become the key to hybrid power, and power management technology is one of the key challenges in the development of aviation hybrid power control systems. This paper reviews the current structural forms of aviation turbine hybrid electric propulsion systems, analyzes the current research status of power management technology for aviation hybrid systems, and points out that the online power management method based on optimization is the best power management technology solution for turbine hybrid electric propulsion systems. Establishing a high-precision and realtime on-board power calculation model, breaking through the power management method based on the integrated flight and engine, and improving the applicability of the power management method throughout the service life are important directions for promoting the development of online power management technology.