This paper has presented an extensive review of the bidirectional phase-modular and semi-modular Solid-State-Transformer (SST) topologies, specific to the matrix-type variants with single-stage AC-DC conversion. This includes a qualitative and mathematical explanation of each topology and the corresponding modulation(s). A comparative analysis incorporating the criteria of power density, failure rate, cost and component count is also done among all these topologies along with the conventional Cascaded-Modular-SST (CMSST) topology with two-stage AC-DC conversion. The matrix-based topologies clearly prove to be better than the CMSST topology in terms of power density and reliability, with the entirely phase-modular topologies proving to be superior overall. The AC-DC DAB type submodule has been estimated to have the best characteristics in terms of all the comparison indices and thus it can be considered to be the best among the grid-connected matrix-based SST topologies for the application-type under consideration. © 2019 IEEE.