We present a review of the searches for very rare decays to muonic final states performed at LHCb using 1.0 fb-1 of pp collisions at 7 TeV centre of mass energy. Flavour changing neutral current processes, such as B->mumu and B->mumumumu are highly suppressed in the Standard Model (SM). Such decays therefore allow contributions from new processes or new heavy particles to significantly modify the expected SM rates. Charged lepton flavour violating processes, such as the neutrino-less tau->mumumu decay, have vanishingly small decay rates in the SM, but can be significantly enhanced in extended models. We report the latest results on these channels from LHCb.