Latest results from LHCb on $B^0_{(s)} \to \mu\mu$ and other very rare decays

In this review I present the latest updates on the searches for very rare decays to muonic final states performed within the LHCb collaboration using pp collisions at 7 and 8 TeV centre of mass energy. Flavour changing neutral current processes, such as $K^0_s \to \mu^+\mu^-, B^0_{(s)} \to \mu^+\mu^-$ and $B^0_{(s)} \to \mu^+\mu^-\mu^+\mu^-$ are highly suppressed in the Standard Model (SM) and are therefore excellent probes of New Physics (NP) processes or heavy particles that can significantly modify the expected SM rates. Out of the many interesting results obtained by the LHCb collaboration in the study of rare decays, this review covers in detail the searches for $K^0_s \to \mu^+\mu^-, B^0_d \to \mu^+ \mu^-$ and $B^0_{(s)} \to \mu^+\mu^-\mu^+\mu^-$ decays and the first evidence for the $B^0_s \to \mu^+\mu^-$ decay.