The rise of the intelligent, local charging facilitation and environmentally friendly aspects of electric vehicles (EVs) has grabbed the attention of many end-users. However, there are still numerous challenges faced by researchers trying to put EVs into competition with internal combustion engine vehicles (ICEVs). The major challenge in EVs is quick recharging and the selection of an optimal charging station. In this paper, we present the most recent research on EV charging management systems and their role in smart cities. EV charging can be done either in parking mode or on-the-move mode. This review work is novel due to many factors, such as that it focuses on discussing centralized and distributed charging management techniques supported by a communication framework for the selection of an appropriate charging station (CS). Similarly, the selection of CS is evaluated on the basis of battery charging as well as battery swapping services. This review also covered plug-in charging technologies including residential, public and ultra-fast charging technologies and also discusses the major components and architecture of EVs involved in charging. In a comprehensive and detailed manner, the applications and challenges in different charging modes, CS selection, and future work have been discussed. This is the first attempt of its kind, we did not find a survey on the charging hierarchy of EVs, their architecture, or their applications in smart cities.