This article presents a review and comparative analysis of converter architectures for electrolyzer systems, covering alternating current (AC) -grid-connected, direct-current (DC) -grid-connected, and renewable-energy-connected systems, as well as isolated and non-isolated configurations. The study classifies and compares key converter topologies based on engineering criteria, including voltage gain, efficiency, device count, control complexity, and implementation feasibility. Furthermore, the relationships among converter structures, power-source characteristics, and electrolyzer-system requirements are analyzed to reveal system-level engineering trade-offs. The analysis demonstrates that converter suitability depends on the combined requirements of the power source, galvanic isolation, electrolyzer characteristics, operating conditions, and application-specific engineering priorities. In addition, wide-bandgap semiconductor devices and electrolyzer operating characteristics are discussed as important factors in converter selection, particularly for improving converter efficiency, reducing current ripple, increasing power density, and supporting dynamic operation. This article therefore provides a systematic framework for converter classification and selection according to power-source characteristics, electrolyzer requirements, and application power levels.