In Sec. 2, we discussed the rigorous theoretical background of molecular cavity QED. We first reviewed the basic theory of the molecular Hamiltonian (Sec. 2.1) and introduced the necessary formalism for molecular quantum electrodynamics (Sec. 2.2). Sec.3 focused on solving the polaritonic eigenvalue equation using various approaches from direct diagonalization in the adiabatic-Fock basis (Sec. Overall, with the recent new capabilities demonstrated in experiments, there has been a recent push to rigorously simulate polariton systems in the strong coupling regime. This has led to a number of theoretical innovations that start to explain and predict these experimental results. However, there are still many mysteries to solve as the systems get increasingly more complex with more molecules and cavity modes. From the theoretical perspective, the singlemolecule case has made significant progress due to the relative numerical simplicity of the simulations compared to highly expensive many-mode and many-molecule (with many electronic levels) simulations that have yet to be fully explored. From the experimental perspective, single-molecule spectroscopy in plasmonic cavities is extremely challenging and has not been widely achieved; however, the results stemming from such simple hybrid systems will afford a much greater leap forward in understanding.