The Chinese–French space mission SVOM (Space-based multiband astronomical Variable Objects Monitor) is mainly designed to detect and localize γ-ray burst (GRB) events. The satellite, to be launched in late 2021, will carry a set of γ-ray, X-ray, and optical imagers. Thanks to its pointing strategy, quick slew capability, and fast data connection to Earth, ground-based observations with large telescopes will allow us to measure redshifts for an unprecedented number of GRBs. While the association of long GRBs with core-collapse supernovae (SNe) is well established, short GRBs are most likely due to neutron star (NS)–NS or NS–BH (black hole) mergers and are thus expected to occur simultaneously with bursts of gravitational waves. We discuss here the overall science goals of the SVOM mission in the framework of the multiwavelength and multimessenger panorama of the next decade.