Rare decays at LHCb

We review recent results from the LHCb experiment on studies of particle decays that are forbidden or rare in the Standard Model. The studies include searches for lepton flavour violating decays of the $\tau$ lepton and the $B$ and $D$ mesons, and of $B$ and $D$ meson decays that would be mediated by Majorana neutrinos. Results are also presented for the rare processes $B_s \to \mu^+\mu^-$ and $B^0 \to \mu^+\mu^-$, $D^0 \to \pi^+\pi^-\mu^+\mu^-$, $b \to s\gamma$ transitions, and $B \to K^{(*)}\mu^+\mu^-$