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 existing experimental results and theoretical approaches, including lattice QCD calculations and semiclassical and quantum approaches for the dynamical evolution of quarkonia in the quark-gluon plasma (QGP) as probed in high-energy heavy-ion collisions. The key ingredients of transport models are detailed to facilitate comparisons of calculated quantities such as reaction rates, binding energies, and nuclear modification factors. The document also assesses the various results and provides an outlook for future research. High-energy nucleus-nucleus collisions, such as those at the Large Hadron Collider (LHC) and Relativistic Heavy-Ion Collider (RHIC), create conditions similar to those in the early universe, particularly the QGP. Quarkonium families, charmonia, and bottomonia, play a crucial role in understanding the fundamental color force in the hot QCD medium. The vacuum heavy-quark (HQ) potential provides a well-calibrated starting point for studying quarkonium interactions in the medium. The string term in the HQ potential characterizes the long-range nonperturbative part of the force and is associated with the confining property of QCD. Quarkonium spectroscopy is used to probe the QCD force in the vacuum, and systematic investigations of different quarkonium states in matter are necessary to understand the in-medium properties of quarkonia. The suppression of charmonia and bottomonia in heavy-ion collisions has been observed at both RHIC and LHC. At RHIC, the suppression of $J/\psi$ production in Au-Au collisions compared to pp collisions was significant, while at LHC, the suppression was reduced in Pb-Pb collisions. The elliptic flow of $J/\psi$ mesons was found to be large at the LHC, suggesting a (re)generation mechanism in the QGP or during hadronization. Bottomonium suppression was also observed, with a similar magnitude at forward rapidity and midrapidity, indicating sequential suppression of excited states. Lattice QCD calculations provide first-principles input for quarkonium production in heavy-ion collisions. Spectral functions, which encode information on quarkonium binding energies and reaction rates, are crucial for understanding the in-medium properties of quarkonia. Effective field theories, such as HQET and pNRQCD, are used to describe the dynamics of heavy quarks and quarkonia in the QGP. Transport models, including the Duke-MIT, Munich-KSU, Nantes, and Saclay models, incorporate these theoretical concepts to simulate quarkonium transport in heavy-ion collisions. These models consider the in-medium potential, reaction rates, and assumptions about the medium to predict quarkonium yields and nuclear modification factorsThis 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 existing experimental results and theoretical approaches, including lattice QCD calculations and semiclassical and quantum approaches for the dynamical evolution of quarkonia in the quark-gluon plasma (QGP) as probed in high-energy heavy-ion collisions. The key ingredients of transport models are detailed to facilitate comparisons of calculated quantities such as reaction rates, binding energies, and nuclear modification factors. The document also assesses the various results and provides an outlook for future research. High-energy nucleus-nucleus collisions, such as those at the Large Hadron Collider (LHC) and Relativistic Heavy-Ion Collider (RHIC), create conditions similar to those in the early universe, particularly the QGP. Quarkonium families, charmonia, and bottomonia, play a crucial role in understanding the fundamental color force in the hot QCD medium. The vacuum heavy-quark (HQ) potential provides a well-calibrated starting point for studying quarkonium interactions in the medium. The string term in the HQ potential characterizes the long-range nonperturbative part of the force and is associated with the confining property of QCD. Quarkonium spectroscopy is used to probe the QCD force in the vacuum, and systematic investigations of different quarkonium states in matter are necessary to understand the in-medium properties of quarkonia. The suppression of charmonia and bottomonia in heavy-ion collisions has been observed at both RHIC and LHC. At RHIC, the suppression of $J/\psi$ production in Au-Au collisions compared to pp collisions was significant, while at LHC, the suppression was reduced in Pb-Pb collisions. The elliptic flow of $J/\psi$ mesons was found to be large at the LHC, suggesting a (re)generation mechanism in the QGP or during hadronization. Bottomonium suppression was also observed, with a similar magnitude at forward rapidity and midrapidity, indicating sequential suppression of excited states. Lattice QCD calculations provide first-principles input for quarkonium production in heavy-ion collisions. Spectral functions, which encode information on quarkonium binding energies and reaction rates, are crucial for understanding the in-medium properties of quarkonia. Effective field theories, such as HQET and pNRQCD, are used to describe the dynamics of heavy quarks and quarkonia in the QGP. Transport models, including the Duke-MIT, Munich-KSU, Nantes, and Saclay models, incorporate these theoretical concepts to simulate quarkonium transport in heavy-ion collisions. These models consider the in-medium potential, reaction rates, and assumptions about the medium to predict quarkonium yields and nuclear modification factors