  The transitions $B_{s,d}\rightarrow \ell^+\ell^-$ (for $\ell=e, \mu, \tau$),
although extremely suppressed within the SM, are exceptionally clean channels
particularly sensitive to New Physics contributions. So far only the branching
ratio for the process $B_{s}\rightarrow \mu^+\mu^-$ has been measured
experimentally and, although the results are in agreement with the SM
prediction, there is still room for NP effects. Here we provide an overview of
the theoretical status of rare decays. We present strategies that can allow us
to discriminate between different NP scenarios. Finally, we include a
discussion of the effects of nontrivial new CP violating phases on the
observables associated with $B_{s}\rightarrow \mu^+\mu^-$.
