Magnetic Coupling Wireless Power Transfer (MCWPT) technology has broad application prospects due to its high degree of freedom in energy exchange and unparalleled security. In recent years, various controllers have been added to WPT systems to improve energy transfer performance. Among them, the Dual-Side Control (DSC) approach, which employs Dual-Active Bridge (DAB) converters with simultaneous control of the transmitter and receiver, has made great progress. The DAB structure has a compromise between cost and complexity, and the DSC can bring a high enough degree of control freedom to the MCWPT system to easily achieve efficiency optimization and desired output characteristics. However, various DSC methods have different characteristics. Therefore, this paper reviews and summarizes the current research status of DSC methods based on the DAB converters in MCWPT systems. Wireless communication is one of the decisive factors in the design of a control strategy, which is categorized in this paper according to the main approaches used in all the papers. Various DSC strategies are described in detail and compared comprehensively according to the control variables and control objectives. This review will be highly beneficial to research entities and industry professionals as a ready reference for the control design in MCWPT.