Energy crisis and environmental problems caused by the conventional combustion of fossil fuels boost the development of renewable and sustainable energies. H2 is regarded as a clean fuel for many applications and it also serves as an energy carrier for many renewable energy sources, such as solar and wind power. Among all the technologies for H2 production, steam electrolysis by solid oxide electrolysis cells (SOECs) has attracted much attention due to its high efficiency and low environmental impact, provided that the needed electrical power is generated from renewable sources. However, the deployment of SOECs based on conventional oxygen-ion conductors is limited by several issues, such as high operating temperature, hydrogen purification from water, and electrode stability. To avoid these problems, proton-conducting oxides are proposed as electrolyte materials for SOECs. This review paper provides a broad overview of the research progresses made for proton-conducting SOECs, summarizing the past work and finding the problems for the development of proton-conducting SOECs, as well as pointing out potential development directions.