This document summarizes the efforts of the EMMI Rapid Reaction Task Force on "Suppression and (re)generation of quarkonium in heavy-ion collisions at the LHC", focusing on their 2019 and 2022 meetings. It reviews experimental results and theoretical approaches, including lattice QCD calculations and semiclassical/quantum methods for quarkonium dynamics in the quark-gluon plasma (QGP). Key ingredients of transport models are itemized to facilitate comparisons of calculated quantities like reaction rates, binding energies, and nuclear modification factors. A diagnostic assessment of results is coupled with an outlook for the future. High-energy nucleus-nucleus collisions create conditions similar to the early universe, allowing study of the QGP and its hadronization. Quarkonium families, charmonia and bottomonia, are critical observables for probing the QCD force. Theoretical models use the vacuum heavy-quark potential, with the string term characterizing nonperturbative forces. Quarkonium can be (re)generated through recombination of heavy quarks and antiquarks in the QGP. Data from LHC and RHIC show suppression of charmonium and bottomonium, with variations in production cross sections and elliptic flow. Theoretical models include transport approaches based on rate equations and semiclassical Boltzmann equations, as well as quantum treatments using open-quantum system frameworks. These models aim to test classical approximations and quantify corrections. Quantum effects are relevant at high transverse momentum, with implications for quarkonium yields. Experimental data from LHC and RHIC show varying suppression patterns for quarkonium states, with significant differences in $ R_{AA} $ and elliptic flow. Lattice QCD results provide insights into quarkonium spectral functions, which encode binding energies and reaction rates. These are used in transport models to study quarkonium dynamics. Theoretical models include the Duke-MIT approach, based on coupled Boltzmann equations, and the Munich-KSU approach, using open quantum system and pNRQCD formalisms. These models aim to describe quarkonium transport in heavy-ion collisions, incorporating in-medium potentials, reaction rates, and transport coefficients. Theoretical and experimental efforts highlight the need for improved models to interpret data from LHC Runs 3 and 4, with a focus on quantum transport treatments and the role of non-perturbative effects in QGP. The study emphasizes the importance of coordinated efforts to advance understanding of quarkonium transport in hot QCD matter.This document summarizes the efforts of the EMMI Rapid Reaction Task Force on "Suppression and (re)generation of quarkonium in heavy-ion collisions at the LHC", focusing on their 2019 and 2022 meetings. It reviews experimental results and theoretical approaches, including lattice QCD calculations and semiclassical/quantum methods for quarkonium dynamics in the quark-gluon plasma (QGP). Key ingredients of transport models are itemized to facilitate comparisons of calculated quantities like reaction rates, binding energies, and nuclear modification factors. A diagnostic assessment of results is coupled with an outlook for the future. High-energy nucleus-nucleus collisions create conditions similar to the early universe, allowing study of the QGP and its hadronization. Quarkonium families, charmonia and bottomonia, are critical observables for probing the QCD force. Theoretical models use the vacuum heavy-quark potential, with the string term characterizing nonperturbative forces. Quarkonium can be (re)generated through recombination of heavy quarks and antiquarks in the QGP. Data from LHC and RHIC show suppression of charmonium and bottomonium, with variations in production cross sections and elliptic flow. Theoretical models include transport approaches based on rate equations and semiclassical Boltzmann equations, as well as quantum treatments using open-quantum system frameworks. These models aim to test classical approximations and quantify corrections. Quantum effects are relevant at high transverse momentum, with implications for quarkonium yields. Experimental data from LHC and RHIC show varying suppression patterns for quarkonium states, with significant differences in $ R_{AA} $ and elliptic flow. Lattice QCD results provide insights into quarkonium spectral functions, which encode binding energies and reaction rates. These are used in transport models to study quarkonium dynamics. Theoretical models include the Duke-MIT approach, based on coupled Boltzmann equations, and the Munich-KSU approach, using open quantum system and pNRQCD formalisms. These models aim to describe quarkonium transport in heavy-ion collisions, incorporating in-medium potentials, reaction rates, and transport coefficients. Theoretical and experimental efforts highlight the need for improved models to interpret data from LHC Runs 3 and 4, with a focus on quantum transport treatments and the role of non-perturbative effects in QGP. The study emphasizes the importance of coordinated efforts to advance understanding of quarkonium transport in hot QCD matter.