The structure and principle of operation of conventional iron-and-copper conventional transformers has not changed for the past decades largely to its high efficiency and reliability. However, conventional transformers are generally heavy and limited to transformation of AC power only in a unidirectional pattern. However, due to the increasing integration of distributed generation to grid, bidirectional power flow within the present grid systems is now inevitable. This makes solid-state transformer (SST), as a more flexible, portable, and cost-effective alternative, to gain considerable attention in recently. The SST is designed using power electronic components and a high frequency transformer (HFT). As an energy router, SST is crucial to the deployment of internet energy system due to its compact size, improved controllability, resiliency, bidirectional power flow, and variety of applications. Various designs and control approaches have been proposed for the SST to suit various applications. Thus, this paper reviews the extent of research works carried out on the SST vis-à-vis classifications, design, control and applications. The review is centered on establishing the state-of-the-art and identify future research prospects in the design, control, and applications of SST.