There exist a multitude of other schemes to approximately solve the TDSE for a realistic system that will not be discussed in this review. However, future applications in simulating polaritonic dynamics will require the use of more accurate methods compared to EH and FSSH. Similar methods to EH exist that are an extension to the Meyer-Miller-Stock-Thoss mapping schemes and lead to methods such as the symmetric quasi-classical (SQC), partially linearized density matrix (PLDM) and later the spin-mapping (SM) approaches, which are all mean-field-level methods in that they treat the forces on the nuclear DOFs as an average over the electronic state population and coherences similar to the EH method but all drastically outperform EH through, for example, the inclusion of zero-point energy (all methods) or using the correct mapping space to constrain the population (sM). Note that many of these approximate quantum dynamics approaches (such as PLDM, SQC, SM, etc.) are formulated in the diabatic representation and are incompatible with adiabatic electronic or polaritonic representation. The recently developed quasidiabatic scheme resolves this issue and allows combining any of these diabatic dynamics approaches with adiabatic electronic or polaritonic representation without requiring any additional non-trivial theoretical efforts such as diabatization. Finally, methods stemming from the exact factorization (XF) formalism, which range from trajectory-based XF surface hopping (XFSH) to coupled trajectory approaches (CTXF), can also be utilized in the polaritonic basis which may lead to additional methods depending on the choice of factorization of the electronic, photonic, and nuclear DOFs. 294-301