The purpose of this review was to introduce and outline state-of-the-art techniques toward the simulation of realistic, ab initio molecular polaritons for readers in the emergent field of polariton chemistry. This review captures much of the recent work, but not all, toward the description of polaritonic states and properties as well as their quantum dynamics. Specifically, this work focused on the methods and approaches needed for one to explore these complicated problems in more depth and did not focus on connecting theory to experiment. While this connection is intrinsic to the answers one seeks from simulation, the discussion of experimental progress and its setbacks is well beyond the scope of this review. We hope this work allows readers of all kinds to dive into the simulation of molecular polaritons to explore the many unknown features of this novel tool to manipulate chemical reactions as well as physical phenomena and to help the community address the many open questions still unexplored by theory and simulation.