With the need for more environmentally friendly transportation and the wide deployment of electric and plug-in hybrid vehicles, electric vehicle (EV) charging stations have become a major issue for car manufacturers and a real challenge for researchers all over the world. Indeed, the high cost of battery energy storage, the limited EV autonomy and battery lifespan, the battery charging time, the deployment cost of a fast charging infrastructure, and the significant impact on the power grid are the origin of several research projects focused on advanced power electronics topologies and the optimization of the EV charging stations in terms of power transfer and geographical location. Three charging levels can be distinguished, which differ in terms of output power and charging time. The higher the level of charging, the faster the charging process, as more power is delivered to the vehicle at the expense of power quality issues and disturbances. Moreover, three types of charging systems can be distinguished, which are inductive recharging (contactless power transfer), conductive charging systems, and battery swapping. Additionally, EVs encompass fuel cell (FC) EVs, which uses hydrogen as primary energy resources, which is nowadays under extensive research activities in academia and industry. This review paper aims at presenting a state of the art review of major advances in power electronics architectures for EVs traction drives, and battery-based EVs charging stations. Specifically, the focus is made on light-duty electric vehicles drivetrain power electronics and charging stations specifications, the proposed power electronics solutions, the advantages and drawbacks of all these technologies, and perspectives for future research works in terms of smart EV charging and up-to-date solutions for power system disturbances mitigation.