  After more than a century of history, the radiation-reaction problem in
classical electrodynamics still surprises and puzzles new generations of
researchers. Here we revise and explain some of the paradoxical issues that one
faces when approaching the problem, mostly associated with regimes of uniform
proper acceleration. The answers we provide can be found in the literature and
are the synthesis of a large body of research. We just present them in a
personal way that may help in their understanding. Besides, after the
presentation of the standard answers we motivate and present a twist to those
ideas. The physics of emission of radiation by extended charges (charges with
internal structure) might proceed in a surprising oscillating fashion. This
hypothetical process could open up new research paths and a new take on the
equivalence principle.
