The isolated AC-AC/DC-AC/AC-DC matrix converter (MC) is an innovative topology with several benefits including minimum current harmonics, nearly unity power factor, four quadrant (4Q) operation, and bidirectional power flow, making it an ideal choice for energy conversion techniques. Unlike any other AC-AC/DC-AC/AC-DC topologies, the MC topology necessitates electrical medium-frequency (MF)/high-frequency (HF) isolation in order to offer single-stage power conversion. MF/HF power conversion topology has numerous advantages such as high-power density, reduced weight, and low noise while preserving converter’s efficiency, cost, and reliability. This paper aims to report an extensive analysis and classification of different conventional isolated single-stage AC-AC converter, DC-AC inverter, and AC-DC rectifier topologies along with their modified system architecture. In this paper, the AC-AC/DC-AC/AC-DC topologies are classified based on their system architecture, AC-side or DC-side drive techniques, and other subvariants. Our primary objective of this study is to impart a clear understanding of the overarching framework and principles of the isolated AC-AC/DC-AC/AC-DC MC topologies and stimulate the creation of new topologies that cater to specific grid-interconnection requirement.