  The in-medium physics of heavy quarkonium is an ideal proving ground for our
ability to connect knowledge about the fundamental laws of physics to
phenomenological predictions. One possible route to take is to attempt a
description of heavy quark bound states at finite temperature through a
Schroedinger equation with an instantaneous potential. Here we review recent
progress in devising a comprehensive approach to define such a potential from
first principles QCD and extract its, in general complex, values from
non-perturbative lattice QCD simulations. Based on the theory of open quantum
systems we will show how to interpret the role of the imaginary part in terms
of spatial decoherence by introducing the concept of a stochastic potential.
Shortcomings as well as possible paths for improvement are discussed.
