A review of old inconsistencies of classical electrodynamics (CED) and some new ideas that solve them is presented. Problems with causality violating solutions of the wave equation, the electron equation of motion, and problems with the non-integrable singularity of its self-field energy tensor are well known. The correct interpretation of the two (advanced and retarded) Lienard - Wiechert solutions are in terms of the creation and annihilation of particles in classical physics. They are both retarded solutions. Previous work on the short-distance limit of CED of a spinless point electron are based on a faulty assumption which causes the well known inconsistencies of the theory: a diverging self-energy (the non-integrable singularity of its self-field energy tensor) and a causality-violating third-order equation of motion (the Lorentz - Dirac equation). The correct assumption fixes these problems without any change in the Maxwell's equations and let exposed, in the zero-distance limit, the discrete nature of light: the flux of energy from a point charge is discrete in time. CED cannot have a true equation of motion, only an effective one, as a consequence of the intrinsic meaning of the Faraday - Maxwell concept of field that does not correspond to the classical description of photon exchange, but only to the smearing of its effects in the space around the charge. This, in varied degrees, is transferred to QED and other field theories that are based on the same concept of fields as space-smeared interactions.