Rare radiative decays at LHCb

Radiative $b$-hadron decays are sensitive probes of New Physics through the study of branching fractions, $CP$ asymmetries and measurements of the polarization of the photon emitted in the decay. During Run I of the LHC, the LHCb experiment has collected large samples of radiative $b$-hadron decays. An overview of the LHCb measurements, including results on the time dependence of $B^0_s \to \phi \gamma$ decays, is presented here. These results help constrain the size of right-handed currents in extensions of the Standard Model.