As this field of cavity quantum electrodynamics (cQED) is highly interdisciplinary drawing from both quantum optics and physical chemistry, the appropriate choice of Hamiltonian can be obfuscated for those new to the field. Often, the relationships between Hamiltonians and exact levels of approximation consequentially become unclear. In this review, we seek to put in one place all the major gauges and representations commonly used in the field in one place with detailed derivations that relate them to each other, helping to bridge the gap between quantum optics and physical chemistry.