This is a discussion of the conceptual problems that have muddled the equation of motion for a radiating charged particle for a long time. An effort is made to pinpoint the weak parts of the usual arguments on this topic. The problems found range from doubts on the applicability of the classical electrodynamics of Maxwell and Lorentz to the problem at hand, to the inapplicability of certain perturbation techniques once the general theory has been tentatively accepted. Hopefully this will raise interest on these challenging problems, whose importance goes beyond the classical domain.