  Heavy-flavor particles are believed to provide valuable probes of the medium
produced in ultrarelativistic collisions of heavy nuclei. In this article we
review recent progress in our understanding of the interactions of charm and
bottom quarks in the Quark-Gluon Plasma (QGP). For individual heavy quarks, we
focus on elastic interactions for which the large quark mass enables a Brownian
motion treatment. This opens a unique access to thermalization mechanisms for
heavy quarks at low momentum, and thus to their transport coefficients in the
quark-gluon fluid. Different approaches to evaluate heavy-quark diffusion are
discussed and compared, including perturbative QCD, effective potential models
utilizing input from lattice QCD and string-theoretic estimates in conformal
field theories. Applications to heavy-quark observables in heavy-ion collisions
are realized via relativistic Langevin simulations, where we illustrate the
important role of a realistic medium evolution to quantitatively extract the
heavy-quark diffusion constant. In the heavy quarkonium sector, we briefly
review the current status in potential-model based interpretations of
correlation functions computed in lattice QCD, followed by an evaluation of
quarkonium dissociation reactions in the QGP. The discussion of the
phenomenology in heavy-ion reactions focuses on thermal model frameworks
paralleling the open heavy-flavor sector. We also emphasize connections to the
heavy-quark diffusion problem in both potential models and quarkonium
regeneration processes.
