  In this report we review recent progress achieved in the understanding of
heavy quarkonium under extreme conditions from a theory perspective. Its focus
lies both on quarkonium properties in thermal equilibrium, as well as recent
developments towards a genuine real-time description, valid also
out-of-equilibrium. We will give an overview of the theory tools developed and
deployed over the last decade, including effective field theories, lattice
field theory simulations, modern methods for spectral reconstructions and the
the open-quantum systems paradigm. The report will discuss in detail the
concept of quarkonium melting, providing the reader with a contemporary
perspective. In order to judge where future progress is needed we will also
discuss recent results from experiments and phenomenological modeling of
quarkonium in relativistic heavy-ion collisions.
