Abstract: Quarkonium has been used as a probe of the quark-gluon plasma (QGP) in heavy ion collisions for decades. To understand the experimental data on quarkonium production, it is important to study the time evolution of quarkonium states inside the plasma. Most phenomenological studies replied on classical rate equations which neglect quantum effects and introduce model dependence in recombination. In this talk, I will review the application of the open quantum system framework to study quarkonium in the QGP. I will explain how the open quantum system framework treats Debye screening, dissociation and recombination in the same theoretical ground and thus removing model dependence in recombination. I will then discuss recent calculations of the chromoelectric field correlators that encode the essential information of the QGP in the quarkonium in-medium dynamics. Finally, I will briefly mention some initial efforts for the quantum simulation of open quantum systems in heavy ion collisions.