  The objective of this paper is to assess the current theoretical
understanding of the extensive set of quarkonium observables (for both
charmonia and bottomonia) that have been attained in ultrarelativistic
heavy-ion collisions over two orders of magnitude in center-of-mass energy. We
briefly lay out and compare the currently employed theoretical frameworks and
their underlying transport coefficients, and then analyze excitation functions
of quarkonium yields to characterize the nature of the varying production
mechanisms. We argue that an overall coherent picture of suppression and
regeneration mechanisms emerges which enables to deduce insights on the
properties of the in-medium QCD force from SPS via RHIC to LHC, and forms a
basis for future quantitative studies.
