Quantum electrodynamics is the well-accepted theory. However, we feel it is useful to look at formalisms that provide alternative ways to describe light, because in the recent years the development of quantum field theories based primarily on the gauge principle has encountered considerable difficulties. There is a wide variety of generalized theories, and they are characterized mainly by the introduction of additional parameters and/or longitudinal modes of electromagnetism. The MajoranaOppenheimer form of electrodynamics, the Sachs theory of Elementary Matter, the analysis of the action-at-a-distance concept, presented recently by Chubykalo and Smirnov-Rueda, and the analysis of the claimed ‘longitudinality’ of the antisymmetric tensor field after quantization are reviewed in this essay. We also list recent advances in the Weinberg 2(2J + 1) formalism (which is built on First Principles) and in the Majorana theory of neutral particles. These may serve as starting points for constructing a quantum theory of light.