Rare decays at LHCb

LHCb has a wide ranging programme of searches for New Physics in rare decays of $B$ and $D$ mesons. Recent highlights are presented, including results of the angular analysis of the decay $B^0 \rightarrow K^{*0} \mu^+\mu^-$ and photon polarization in the $B^+\rightarrow K^+ \pi^-\pi^+\gamma$ process. We also report about the observation of a resonance in the decay $B^+ \rightarrow K^+ \mu^+\mu^-$ at low recoil.