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

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 Standard Model, specially in the scalar and pseudoscalar sector. The recent, most sensitive measurements from the CDF, ATLAS, CMS and LHCb collaborations are discussed and the combined upper exclusion limit on the branching fractions determined 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 Physics models is sketched.