New incarnations of heavy-ion collision experiments are turning our attention to hard processes and a more fine-grained resolution of the QGP. In this endeavor quarkonia or open heavy flavors turn out to be versatile probes, which are usually described through models based on perturbative QCD, AdS, and effective field theories. The lattice provides nonperturbative input and constraints to such models.
In-medium bottomonia, the complex static quark-antiquark potential, and the heavy-quark momentum diffusion coefficient are key quantities where lattice gauge theory has recently achieved significant progress with impact for heavy-ion phenomenology. We review these lattice results, relate them to phenomenological applications, and close with an outlook.