Theory overview of $B_{s,d}\to \mu^+\mu^-$ decays

In this talk I give a theoretical overview of the rare decays $B_{s} \to \mu^+ \mu^-$ and $B_{d} \to \mu^+ \mu^-$. The branching ratios of these decays are promising probes of New Physics, both independently and relative to each other. Recent experimental progress at the LHC has confirmed the existence of the $B_{s} \to \mu^+ \mu^-$ decay, and has not revealed any large signals of New Physics that may have been present. This raises the question of whether moderate New Physics effects can be identified in the LHC era. To that end I review several important developments in the Standard Model branching ratio predictions, and discuss how the latest measurements currently constrain New Physics. Furthermore, I highlight how a time-dependent analysis of $B_{s} \to \mu^+ \mu^-$, which may be feasible at the upgraded CMS and LHCb detectors, can complement the search for and identification of New Physics.