The purpose of this review is to introduce and outline state-of-the-art techniques toward the simulation of realistic, ab initio molecular polaritons for the 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 focuses on the methods and approaches needed for one to explore these complicated problems in more depth and does not primarily 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 beyond the scope of this review aimed at ab initio computational approaches. We hope that this work allows readers of all kinds to becomes acquainted with the simulation of molecular polaritons to explore the the many unknown possibilities this novel tool has in order to manipulate chemical reactions as well as physical phenomena and to help the community to address the many open questions still unexplored by theory and simulation.