Here, we have depicted only one possible way of performing exact polaritonic dynamics; however, many other exact (or almost exact) quantum dynamics approaches exist that can be utilized. In the following we will mention a few of these approaches: The Multi-configuration time-dependent Hartree (MCTDH) scheme has been recently used to simulate polariton photochemistry, 222 conical intersections in cavity and vibrational polariton dynamics. The exact factorization (XF) approach has only recently been developed and has been to used to simulate polariton photochemistry giving rise to novel interpretations of the wavefunction and the exact potential energy surface depending on the choice of factorization of the electronic, photonic, and nuclear DOFs. The hierarchical equation of motion (HEOM) approach has been used to simulate conical intersection inside cavity 227 and vibrational polariton chemistry. Additionally, ab initio multiple spawning (AIMS), Ehrenfest multiple cloning (EMC), and their variants 232-234 could also be adapted for polaritonic dynamics to give nearly exact results.