Nowadays, the imperative need for the reduction of Greenhouse Gas (GHG) emissions leads to the wider adoption of environmentally friendly transportation means. As a result, various policies underpinning the Electric Vehicle (EV) deployment are legislated globally, and several technical advances contributing to the electrification of the transportation sector are pursued. In this paper, a comprehensive overview of the current status of the infrastructure utilized for the realization of both conductive and contactless (wireless) charging of an EV battery is conducted. Furthermore, the issue of EV integration in conventional distribution networks, as well as in future power system architectures, is discussed in detail. Particular focus is given to wireless (i.e., inductive) charging. A detailed presentation of the respective standards and charging levels, as well as the magnetic couplers and the compensation network configurations, is carried out. Moreover, innovative concepts such as dynamic and quasi-dynamic wireless charging, as well as future challenges and opportunities, are presented and discussed. Finally, smart control and communication techniques applicable to EV charging are presented in the context of the future Internet of Energy (IoE) concept.