Proton-conducting ceramic materials have emerged as effective candidates for improving the performance of solid oxide cells (SOCs) and electrolyzers (SOEs) at intermediate temperatures. BaCeO3 and BaZrO3 perovskites doped with rare-earth elements such as Y2O3 (BCZY) are well known for their high proton conductivity, low operating temperature, and chemical stability, which lead to SOCs’ improved performance. However, the high sintering temperature and extended processing time needed to obtain dense BCZY-type electrolytes (typically > 1350 °C) to be used as SOC electrolytes can cause severe barium evaporation, altering the stoichiometry of the system and consequently reducing the performance of the final device. The cold sintering process (CSP) is a novel sintering technique that allows a drastic reduction in the sintering temperature needed to obtain dense ceramics. Using the CSP, materials can be sintered in a short time using an appropriate amount of a liquid phase at temperatures < 300 °C under a few hundred MPa of uniaxial pressure. For these reasons, cold sintering is considered one of the most promising ways to obtain ceramic proton conductors in mild conditions. This review aims to collect novel insights into the application of the CSP with a focus on BCZY-type materials, highlighting the opportunities and challenges and giving a vision of future trends and perspectives.