Owing to the constantly rising energy demand, Internal Combustion Engine (ICE)-equipped vehicles are being replaced by Electric Vehicles (EVs). The other advantage of using EVs is that the batteries can be utilised as an energy storage device to increase the penetration of renewable energy sources. Integrating EVs with the grid is one of the recent advancements in EVs using Vehicle-to-Grid (V2G) technology. A bidirectional technique enables power transfer between the grid and the EV batteries. Moreover, the Bidirectional Wireless Power Transfer (BWPT) method can support consumers in automating the power transfer process without human intervention. However, an effective BWPT requires a proper vehicle and grid coordination with reasonable control and compensation networks. Various compensation techniques have been proposed in the literature, both on the transmitter and receiver sides. Selecting suitable compensation techniques is a critical task affecting the various design parameters. In this study, the basic compensation topologies of the Series–Series (SS), Series–Parallel (SP), Parallel–Parallel (PP), Parallel–Series (SP), and hybrid compensation topology design requirements are investigated. In addition, the typical control techniques for bidirectional converters, such as Proportional–Integral–Derivative (PID), sliding mode, fuzzy logic control, model predictive, and digital control, are discussed. In addition, different switching modulation schemes, including Pulse-Width Modulation (PWM) control, PWM + Phase Shift control, Single-Phase Shift, Dual-Phase Shift, and Triple-Phase Shift methods, are discussed. The characteristics and control strategies of each are presented, concerning the typical applications. Based on the review analysis, the low-power (Level 1/Level 2) charging applications demand a simple SS compensation topology with a PID controller and a Single-Phase Shift switching method. However, for the medium- or high-power applications (Level 3/Level 4), the dual-side LCC compensation with an advanced controller and a Dual-Side Phase-Shift switching pattern is recommended.