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The current experimental status of the searches for the very rare decays$B^0_s \rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$ is discussed.These channels are highly sensitive to various extensions of the StandardModel, specially in the scalar and pseudoscalar sector. The recent, mostsensitive measurements from the CDF, ATLAS, CMS and LHCb collaborations arediscussed and the combined upper exclusion limit on the branching fractionsdetermined by the LHC experiments is shown to be $4.2\times 10^{-9}$ for $B^0_s\rightarrow \mu^+ \mu^-$ and $0.8\times 10^{-9}$ for $B^0 \rightarrow \mu^+\mu^-$. The implications of these tight bounds on a selected set of New Physicsmodels is sketched.

Brief review of the searches for the rare decays $B^0_s \rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$