Electric vehicles (EVs) are becoming more popular worldwide due to environmental concerns, fuel security, and price volatility. The performance of EVs relies on the energy stored in their batteries, which can be charged using either AC (slow) or DC (fast) chargers. Additionally, EVs can also be used as mobile power storage devices using vehicle-to-grid (V2G) technology. Power electronic converters (PECs) have a constructive role in EV applications, both in charging EVs and in V2G. Hence, this paper comprehensively investigates the state of the art of EV charging topologies and PEC solutions for EV applications. It examines PECs from the point of view of their classifications, configurations, control approaches, and future research prospects and their impacts on power quality. These can be classified into various topologies: DC-DC converters, AC-DC converters, DC-AC converters, and AC-AC converters. To address the limitations of traditional DC-DC converters such as switching losses, size, and high-electromagnetic interference (EMI), resonant converters and multiport converters are being used in high-voltage EV applications. Additionally, power-train converters have been modified for high-efficiency and reliability in EV applications. This paper offers an overview of charging topologies, PECs, challenges with solutions, and future trends in the field of the EV charging station applications.