Descriptions of optical beams with structured wavefronts or vector polarizations are widely cast in terms of classical field theory. The corresponding fully quantum counterparts often present new insights into what is physically observed, and they are especially of interest when tackling issues such as entanglement. Similarly, when determining angular momentum densities, it appears that the separate roles of photon spin and beam topological charge can only be satisfactorily addressed within a quantum framework. In some such respects, the quantum versions of theory might be considered to introduce an additional layer of complexity; in others, they can clearly and very substantially simplify the theoretical representation. At the photon level, the fully quantized descriptions of topologically structured and singular beams nonetheless raise important fundamental questions and puzzles, whose resolution continue to invite attention. Many of the mechanistic interpretations and predictions (those that appear to be supported by a true congruence between classic and quantum optical descriptions, essentially conflating electromagnetic field and state wavefunction concepts) can lead to theoretical pitfalls. This paper highlights some physical implications that emerge from a fully quantum treatment of theory.