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The bound states of a heavy quark and antiquark ($c\bar{c}, b\bar{b}$) areideal probes to explore the quark-gluon plasma created in relativisticheavy-ion collisions at the RHIC and LHC. Not only have they becomeexperimentally accessible with high precision but also efficient tools, socalled effective field theories (EFT) have been developed to treat themtheoretically. Here we present recent progress in understanding the in-mediumbehavior of heavy-quarkonium with the help of EFT's combined withnon-perturbative and first principles simulations in lattice QCD. In particularwe discuss computations of heavy quarkonium spectral functions with the help ofBayesian unfolding methods and the physics we can extract from them.Limitations and the underlying assumptions of the used approaches are pointedout.

What lattice QCD spectral functions can tell us about heavy quarkonium in the QGP