A review and discussion of both the historical and contemporaneous ideas pertaining to the putative population of Vulcanoid asteroids is presented. Current observations indicate that no objects larger than between 5 to 10 km in diameter reside in the orbital stability zone between 0.06 and 0.2 AU from the Sun, and that, at best, only a small population of Vulcanoid asteroids might exist at the present epoch. We review the physical processes (sublimation mass loss, evolution of the Sun’s luminosity, Poynting-Robertson drag, the Yarkovsky effect, the YORP effect, unipolar heating and collisions) that will control the lifetime against destruction of objects, either primordial or present-day, that chance to reside in the Vulcanoid region. It is argued that there are no overriding and/or absolute physical mechanisms that fully rule-out the present-day existence of a small Vulcanoid population, but we note that the gap between what the observations allow and what the theoretical models deem possible is closing rapidly.