Hydrogen sulfides have recently received a great deal of interest due to the record high superconducting temperatures of up to 203 K observed on strong compression of dihydrogen sulfide (H2S). A joint theoretical and experimental study is presented in which decomposition products and structures of compressed H2S are characterized, and their superconducting properties are calculated. In addition to the experimentally known H2S and H3S phases, our first-principles structure searches have identified several energetically competitive stoichiometries that have not been reported previously: H2S3, H3S2, HS2, and H4S3. In particular, H4S3 is predicted to be thermodynamically stable within a large pressure range of 25–113 GPa. High-pressure x-ray diffraction measurements confirm the presence of H3S and H4S3 through decomposition of H2S that emerges at 27 GPa and coexists with residual H2S, at least up to the highest pressure of 140 GPa studied in our experiments. Electron-phonon coupling calculations show that H4S3 has a small Tc of below 2 K, and that H2S is mainly responsible for the observed superconductivity of samples prepared at low temperature (<100 K).