The increasing emissions created by the large-scaled number of automobiles around the world pose severe threats to modern life by causing global warming issues and deteriorating air quality. These serious issues stimulate the essential demand for cleaner, safer, and more efficient vehicles, such as battery electric vehicles (BEVs). Unlike other studies on the charging technologies of BEVs, this paper gives a comprehensive state-of-the-art review on the charging technologies available for BEVs: wired charging and wireless charging technologies. First, the wired charging technologies are systematically classified into AC charging (indirect charging) and DC charging (direct charging) methods based on how the BEVs batteries are fed from the grid. Next, the configurations and commonly used topologies of wireless charging technologies for BEVs are thoroughly discussed. The leading institutes/companies driving advancements in both technologies are also acknowledged. Finally, this paper extensively highlights the recent and future research trends along with the industrial applications. INDEX TERMS AC charging, battery electric vehicles (BEVs), DC charging, off-board charger, on-board charger (OBC), wired charging, wireless charging.