Abstract: Inductively coupled power transfer (ICPT) technology is the earliest research start, the fastest practical and commercial progress, and the most widely used technical route in the technology of wireless power transfer. However, an important issue that affects its practicability is the load and coupling sensitivity problem. How to improve the output stability of the ICPT system under variable coupling or load conditions has always been the focus of the research. The compensation topologies can reduce the reactive power of the system and improve the energy transmission efficiency and load capacity of the system. With the reasonable topology design and parameter optimization design of the compensation network, the system can have the characteristics of coupling and load independence. The research on compensation network of ICPT system under variable parameters conditions can enhance the practicality of the ICPT technology. This paper summarized not only the related researches on the compensation topologies of the ICPT system under variable parameters conditions but also its topology design methods and parameter optimization methods according to the classification of load-independent, coupling-independent, and coupling-load independent. Its future research direction was also discussed.