Motivated by the observation of the decay B̄→K̄*γ by the CLEO Collaboration, we have systematically analyzed the two-body weak radiative decays of bottom and charmed hadrons. There exist two types of weak radiative decays: One proceeds through the short-distance b→sγ transition and the other occurs through W exchange accompanied by a photon emission. Effective Lagrangians are derived for the W-exchange bremsstrahlung processes at the quark level and then applied to various weak electromagnetic decays of heavy hadrons. Predictions for the branching ratios of B̄0→D*0γ, Λb0→c0γ, Ξb0→Ξc0γ, and Ξb0→Ξ'b0γ are given. In particular, we find scrB(B̄0→D*0γ)0.9×10-6. Order of magnitude estimates for the weak radiative decays of charmed hadrons, D0→K̄*0γ, Λc+→+γ, and Ξc0→Ξ0γ, are also presented. Within this approach, the decay asymmetry for antitriplet to antitriplet heavy baryon weak radiative transitions is uniquely predicted by heavy quark symmetry. The electromagnetic penguin contribution to Λb0→Λγ is estimated by two different methods and its branching ratio is found to be of the order of 1×10-5. We conclude that weak radiative decays of bottom hadrons are dominated by the short-distance b→sγ mechanism.