This review summarizes the current experimental results on rare B0_(s) -> mu+mu- decays of the Tevatron experiments CDF and D0, and the LHC experiments ATLAS, CMS and LHCb. The experimental branching fraction upper limits for the B0_s -> mu+mu- are a
lready quite close to the branching fraction predicted by the Standard Model, and the first observation of the B0_s -> mu+mu- decay is expected soon. The rare decays B0_(s) -> mu+mu- are highly suppressed in the Standard Model, and therefore accurate measurements of these branching fractions provide complementary constraints to the free parameters of various extensions of the Standard Model.
