  Heavy quarks, and the hadrons containing them, are excellent probes of the
QCD medium formed in high-energy heavy-ion collisions, as they provide direct
information on the transport properties of the medium and how quarks
color-neutralize into hadrons. Large theoretical and phenomenological efforts
have been dedicated thus far to assess the diffusion of charm and bottom quarks
in the quark-gluon plasma and their subsequent hadronization into heavy-flavor
(HF) hadrons. However, the fireball formed in heavy-ion collisions also
features an extended hadronic phase, and therefore any quantitative analysis of
experimental observables needs to account for rescattering of charm and bottom
hadrons. This is further reinforced by the presence of a QCD cross-over
transition and the notion that the interaction strength is maximal in the
vicinity of the pseudo-critical temperature. We review existing approaches for
evaluating the interactions of open HF hadrons in a hadronic heat bath and the
pertinent results for scattering amplitudes, spectral functions and transport
coefficients. While most of the work to date has focused on $D$ mesons, we also
discuss excited states as well as HF baryons and the bottom sector. Both the HF
hadro-chemistry and bottom observables will play a key role in future
experimental measurements. We also conduct a survey of transport calculations
in heavy-ion collisions that have included effects of hadronic HF diffusion and
assess their sensitivity to various observables.
