Rare decays in CMS

Studies of rare decays play an important role in the search for physics beyond the standard model. Recent results from the CMS experiment on the decays of B and $\tau$ particles to final states containing muons, based on 8 and 13 TeV data, are presented. In addition, the perspectives for the measurements of the $B^0_s\to\mu^+\mu^-$ and $B^0\to\mu^+\mu^-$ branching fractions and $B^0\to\mu^+\mu^-$ effective lifetime at the High-Luminosity LHC are reported, together with the projections for the sensitivity of the $P_5'$ parameter in the $B^0 \to K^{0*}\mu^+\mu^-$ angular analysis.