This paper provides a comprehensive review and outlook on power converters devised for supplying polymer electrolyte membrane (PEM) electrolyzers from photovoltaic sources. The produced hydrogen, known as green hydrogen, is a promising solution to mitigate the dependence on fossil fuels. The main topologies of power conversion systems are discussed and classified; a loss analysis emphasizes the issues concerning the electrolyzer supply. The attention is focused on power converters of rated power up to a tenth of a kW, since it is a promising field for a short-term solution implementing green hydrogen production as a decentralized. It is also encouraged by the proliferation of relatively cheap photovoltaic low-power plants. The main converters proposed by the literature in the last few years and realized for practical applications are analyzed, highlighting their key characteristics and focusing on the parameters useful for designers. Future perspectives are addressed concerning the availability of new wide-bandgap devices and hard-to-abate sectors with reference to the whole conversion chain.