Solid-state transformers (SSTs) are an emerging technology that has been developed for modern distribution systems. These new transformers are composed of a medium ac voltage (MV) stage, a dc stage, and a low ac voltage (LV) stage. Passive and active dc-links are used in SSTs to support new transformer functionalities, including hybrid (ac and dc) distribution, reactive power compensation, voltage/frequency regulation, power quality improvement, and distributed generation interconnection. However, a SST has to have one of its stages connected to a MV level, which mandates certain converter topologies and/or switching element capabilities. In addition, the dc-link stage has to provide isolation between the MV and LV levels, which requires the employment of isolated dc-dc power electronic converters (PECs). This paper provides a review of SSTs for distribution systems, in terms of the required technology, possible functionalities, performance, and challenges for SSTs and their host distribution systems.