Hydrogen-rich compounds are promising candidates for high-Tc or even room-temperature superconductors.The search for high-Tc hydrides poses a major experimental challenge because there are many known hydrides and even more unknown hydrides with unusual stoichiometries under high pressure.The combination of crystal structure prediction and first-principles calculations has played an important role in the search for high-Tc hydrides,especially in guiding experimental synthesis.Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) is one of the most efficient methods for predicting stable or metastable structures from the chemical composition alone.This review summarizes the superconducting hydrides predicted using CALYPSO.We focus on two breakthroughs toward room-temperature superconductors initiated by CALYPSO:the prediction of high-Tc superconductivity in compressed hydrogen sulfide and lanthanum hydrides,both of which have been confirmed experimentally and have set new record Tc values.We also address the challenges and outlook in this field.