Radiative $b$-hadron decays proceed via the flavour-changing neutral-current transitions $b\rightarrow s\gamma$ and $b\rightarrow d\gamma$, which are forbidden at tree level in the Standard Model and occur only through loop diagrams. As a result, they provide powerful probes of physics beyond the Standard Model. Radiative decays offer a large set of observables, including measurements of branching fractions, charge-parity violation, angular distributions and photon polarization, sensitive to different beyond the Standard Model scenarios. This document presents the most precise measurement of the $B^0\to\rho(770)^0\gamma$ decay branching fraction, the first evidence for the $B_s^0\to K^-\pi^+\gamma$ decay and the search for the $B^0_{(s)}\to J/\psi\gamma$ decays at LHCb.