  In this white paper for the Snowmass process, we review the status and
prospects of the field of rare decays of b and c hadrons. The role that rare
decays play in the search for physics beyond the Standard Model is emphasised.
We stress the complementarity of a large set of relevant processes and outline
the most promising directions. The experimental opportunities at Belle II, BES
III, ATLAS, CMS, LHCb, and at future machines are discussed. We also summarize
the challenges that need to be addressed on the theory side to achieve theory
uncertainties for rare decays that match the expected experimental
sensitivities.
