The weak equivalence principle (WEP) is the cornerstone of general relativity (GR). Testing it is thus a natural way to confront GR to experiments, which has been pursued for four centuries with increasing precision. MICROSCOPE is a space mission designed to test the WEP with a precision of 1 in 1015 parts, two orders of magnitude better than previous experimental constraints. After completing its two-year mission, from 2016 to 2018, MICROSCOPE delivered unprecedented precise constraints $\eta(\mathrm{Ti, Pt}) = [-1.5 \pm 2.3~\mathrm{(stat)} \pm 1.5~\mathrm{(syst)}] \times 10^{-15}$ (at 1σ in statistical errors) on the Eötvös parameter between one proof mass made of titanium and another made of platinum. This bound allowed for improved constraints on alternative theories of gravitation. This review discusses the science beyond MICROSCOPE—GR and its alternatives, with an emphasis on scalar–tensor theories—before presenting the experimental concept and apparatus. The mission's science returns are then discussed before future tests of the WEP are introduced.