Increase in global energy demand and constraints from fossil fuels have encouraged a growing share of renewable energy resources in the utility grid. Accordingly, an increased penetration of direct current (DC) power sources and loads (e.g., solar photovoltaics and electric vehicles) as well as the necessity for active power flow control has been witnessed in the power distribution networks. Passive transformers are susceptible to DC offset and possess no controllability when employed in smart grids. Solid state transformers (SSTs) are identified as a potential solution to modernize and harmonize alternating current (AC) and DC electrical networks and as suitable solutions in applications such as traction, electric ships, and aerospace industry. This paper provides a complete overview on SST: concepts, topologies, classification, power converters, material selection, and key aspects for design criteria and control schemes proposed in the literature. It also proposes a simple terminology to identify and homogenize the large number of definitions and structures currently reported in the literature.