  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 already 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.
