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.

94 pages, 41 figures, 2 tables; invited review for chapter in "Quark-Gluon Plasma 4"; comments welcome; v2: additional references, streamlined text