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Researchers worldwide have become increasingly interested in developing computational approaches to handle challenges facing electric vehicles (EVs) in recent years. This article examines the challenges and future potential of computational approaches for problems such as EV routing, EV charging scheduling (EVCS), EV charging station (CS) placement, CS sizing, and energy or load management. In addition, a summary of the fundamental mathematical models employed to solve the EV computational problems is presented. We cover recent work on computational solutions for various EV problems utilizing single and coupled mathematical models. Finally, we also examine potential research avenues that researchers could pursue to realize the objective of environment-friendly transportation and smart grids (SGs).