Rare decays of $\Lambda_b^0$, $B_c^+$, and other $b$-hadrons at LHCb

Rare $b$-hadron decays are sensitive probes of New Physics through the study of branching fractions, angular observables and CP asymmetries among others. Moreover, the LHCb experiment has the opportunity to study rare decays of heavy b-quark hadrons such as $\Lambda_b$ baryons, which cannot be explored at the B factories. Recent results from the LHCb experiment are presented and their interpretation is discussed.