The growing trend for electric vehicles (EVs) and fast-charging stations (FCSs) will cause the overloading of grids due to the high current injection from FCSs’ converters. The insensitive nature of the state of charge (SOC) of EV batteries during FCS operation often results in grid instability problems, such as voltage and frequency deviation at the point of common coupling (PCC). Therefore, many researchers have focused on two-stage converter control (TSCC) and single-stage converter (SSC) control for FCS stability enhancement, and suggested that SSC architectures are superior in performance, unlike the TSCC methods. However, only a few research works have focused on SSC techniques, despite the techniques’ ability to provide inertia and damping support through the virtual synchronous machine (VSM) strategy due to power decoupling and dynamic response problems. TSCC methods deploy current or voltage control for controlling EVs’ SOC battery charging through proportional-integral (PI), proportional-resonant (PR), deadbeat or proportional-integral-derivative (PID) controllers, but these are relegated by high current harmonics, frequency fluctuation and switching losses due to transient switching. This paper reviewed the linkage between the latest research contributions, issues associated with TSCC and SSC techniques, and the performance evaluation of the techniques, and subsequently identified the research gaps and proposed SSC control with SOC consideration for further research studies.