  The problem of quarkonium production in heavy ion collisions presents a set
of unique theoretical challenges -- from the relevant production mechanism of
$J/\psi$ and $\Upsilon$ to the relative significance of distinct cold and hot
nuclear matter effects in the observed attenuation of quarkonia. Inthese
proceedings we summarize recent work on the generalization of non-relativistic
Quantum Chromodynamics (NRQCD) to include off-shell gluon (Glauber/Coulomb)
interactions in strongly interacting matter. This new effective theory provides
for the first time a universal microscopic description of the in-medium
interaction of heavy quarkonia, consistently applicable to a range of phases
such as cold nuclear matter, dense hadron gas, and quark-gluon plasma. It is an
important step forward in understanding the common trends in proton-nucleus and
nucleus-nucleus data on quarkonium suppression. We derive explicitly the
leading and sub-leading interaction terms in the Lagrangian and show the
connection of the leading result to existing phenomenology.
