Electric propulsion (EP) has become a pivotal technology in modern space exploration, enabling prolonged mission durations, increased payload capacity, and precise deep-space navigation through its superior thrust efficiency and low propellant consumption. However, the performance of EP systems is fundamentally limited by the power processing unit (PPU), with the DC-DC power converter serving as the core of the PPU. Existing research on DC-DC converters often focuses on generic topologies, failing to address the divergent power demands of distinct EP types and the harsh space-specific constraints. This review aims to fill this gap by systematically analyzing DC-DC power converters tailored for EP systems. First, the core requirements of converters across major EP categories are classified. Then, converter topologies are compared by evaluating the suitability for EP operational and space constraints. Moreover, high step-up conversion techniques are explored that bridge the gap between low-voltage spacecraft buses and thruster power needs. Furthermore, this review highlights emerging technologies driving EP converter advancement, such as wide-bandgap semiconductors for improved power density and efficiency, planar magnetics for miniaturization, and direct-drive architecture for simplified Hall-effect thruster integration. It also identifies unresolved challenges, including balancing power density with thermal robustness, mitigating radiation-induced degradation, and suppressing electromagnetic interference (EMI). Finally, it outlines future research directions, such as optimizing WBG-compatible converter topologies, developing advanced thermal management solutions, and standardizing EP-specific design guidelines. This work provides a practical reference for PPU engineers, linking converter design to EP unique demands and space constraints while guiding innovations to advance EP technology for next-generation space missions, from low-Earth orbit satellites to interplanetary exploration.