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The increasing demand for wireless power transfer (WPT) systems for electric vehicles (EVs) has necessitated advancements in charging solutions, with a particular focus on speed and efficiency. However, power transfer efficiency is the major concern in static and dynamic wireless charging (DWC) design. Design consideration and improvements in all functional units are necessary for an increase in overall efficiency of the system. Recently, different research works have been presented regarding DWC at the power converter, coil structure and compensators. This paper provides a comprehensive review of power converters incorporating high-order compensation topologies, demonstrating their benefits in enhancing the DWC of EVs. The review also delves into the coupling coil structure and magnetic material architecture, pivotal in enhancing power transfer efficiency and capability. Moreover, the high-order compensation topologies used to effectively mitigate low-frequency ripple, improve voltage regulation, and facilitate a more compact and portable design are discussed. Furthermore, optimal coupling and different techniques to achieve maximum power transfer efficiency are discussed to boost magnetic interactions, thereby reducing power loss. Finally, this paper highlights the essential role of these components in developing efficient and reliable DWC systems for EVs, emphasizing their contribution to achieving high-power transfer efficiency and stability. [ABSTRACT FROM AUTHOR]