  In this paper we review recent progress towards understanding the nature of
quarkonia in the quark-gluon plasma. We review the theory necessary to
understand the melting of bound states due to color-screening, including
lattice results for the heavy quark potential, lattice results on the
correlation functions related to the relevant spectral functions, and the
emergence of a complex-valued potential in high-temperature quantum
chromodynamics. We close with a brief survey of phenomenological models of
quarkonium suppression in relativistic heavy ion collisions.
