The emergence of DC fast chargers for electric vehicle batteries (EVBs) has prompted the design of ad-hoc microgrids (MGs), in which the use of a solid-state transformer (SST) instead of a low-frequency service transformer can increase the efficiency and reduce the volume and weight of the MG electrical architecture. Mimicking a conventional gasoline station in terms of service duration and service simultaneity to several customers has led to the notion of ultra-fast chargers, in which the charging time is less than 10 min and the MG power is higher than 350 kW. This survey reviews the state-of-the-art of DC ultra-fast charging stations, SST transformers, and DC ultra-fast charging stations based on SST. Ultra-fast charging definition and its requirements are analyzed, and SST characteristics and applications together with the configuration of power electronic converters in SST-based ultra-fast charging stations are described. A new classification of topologies for DC SST-based ultra-fast charging stations is proposed considering input power, delta/wye connections, number of output ports, and power electronic converters. More than 250 published papers from the recent literature have been reviewed to identify the common understandings, practical implementation challenges, and research opportunities in the application of DC ultra-fast charging in EVs. In particular, the works published over the last three years about SST-based DC ultra-fast charging have been reviewed.