To guarantee mission success and minimize the risk of anomalies in space, current space-power architectures are designed conservatively and use electronics that are several generations behind the current state of the art. In parallel, the commercial industry is burgeoning with exciting new solutions for power management; however, their reliability and radiation robustness for space application have yet to be proven. The goal of this paper is to review common radiation issues related to power converters, which are the main design blocks of current space power system architectures. We first provide some background material and introduce the basic principles of power converter operation, as well as a brief introduction of common radiation effect that might damage these designs. Then, we explain common radiation-induced failure mechanisms (radiation-induced failure or instability) or temporary perturbations observed in various converter topologies. Their radiation hardness is compared based on simulation and experimental studies reported in the literature. Some radiation hardening by design solutions and mitigation techniques are also presented. Finally, we provide a status of emerging technologies under consideration for the next-generation of space power systems.