Capturing higher-order correlations between electrons has a well-defined procedure using post-HF approaches, such as configuration interaction (CI) or coupled cluster (CC) expansions in the basis of excited Slater determinants. The polaritonic community has also used such wavefunction approaches for computing the polaritonic electronic-bosonic states in addition to other approaches such as time-dependent DFT (TD-DFT), reduced density matrix (RDM) theory, 106 quantum Monte Carlo, 107 Møller-Plesset Theory (MP-n), and density matrix renormalization group (DMRG). 108;109;110;80 While mean-field approaches (e.g., HF, DFT) yield useful ground state information, even in the absence of correlation, it is not yet clear to what extent the correlated excitations of the matter and photonic DOFs will impact the results, even in the ground polaritonic state. Further, the need for polaritonic excited states is ubiquitous in the photophysics and photochemistry of excited polaritons. Additionally, the determination of the light-matter coupling strength is often predicated on the magnitude of the Rabi splitting between the light and matter excitations at resonance. While our goal is not to outline all possible many-body approaches which go beyond mean-field, we will briefly outline and discuss QED coupled cluster theory (QED-CCSD) since in the electronic structure community coupled cluster theory is one of the most widely used approximations for capturing electronic correlation in a wide variety of molecules.