The SHiP Collaboration has proposed a general-purpose experimental facility operating in beam dump mode at the CERN SPS accelerator with the aim of searching for light, long-lived exotic particles. The detector system aims at measuring the visible decays of hidden sector particles to both fully reconstructible final states and to partially reconstructible final states with neutrinos, in a nearly background free environment. In addition to that, it can detect light dark matter via its scattering and study tau neutrino physics. Using a high-intensity beam of 400 GeV protons, the experiment is capable of integrating $2 \times 10^{20}$ protons in five years, which allows probing dark photons, dark scalars, axion-like particles and heavy neutral leptons with GeV-scale masses at sensitivities that exceed by orders of magnitude those of existing and projected experiments. The sensitivity to heavy neutrinos will allow for the first time to probe, in the mass range between the kaon and the charm meson mass, a coupling range for which baryogenesis and the magnitude of the active neutrino masses can be explained. The sensitivity to light dark matter reaches well below the elastic scalar dark matter relic density limits in the range from a few MeV/c$^2$ up to 200 MeV/c$^2$.