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Electric vehicles (EV) are found to be a good alternative for the conventional internal combustion (IC) engine vehicles in transportation sector due to its various advantages. Now-a-days, wireless charging of EV battery is preferred among the various methods used for charging EV battery. In this paper, extensive review is carried out on various methods used for wireless charging of an EV battery. Different techniques used for transferring power in wireless mode to charge the EV battery are static EV charging technique and dynamic EV charging technique. Static wireless EV battery charging technique adopts inductive and capacitive method for transferring power whereas, dynamic wireless EV battery charging technique adopts only inductive method for transferring power. These techniques are discussed thoroughly in this paper and broad review is carried out with a focus on the compensation circuit topologies, types of core for magnetic coupled inductors, different converters and controllers used for wireless power transfer (WPT) system. Also, design aspects of an static wireless EV battery charging system along with its equivalent circuit analysis is presented in this paper. Challenges and future development in wireless charging of EV battery is also explained in this paper.