The paper reviews the radiation phenomena in classical electromagnetics in terms of microscopic and macroscopic approach, respectively. First, the radiation from an accelerated charged particle is outlined featuring the concept of radiation reaction force. Then the Pocklington integro-differential equation for dipole antennas is derived which is followed by the details related to the numerical solution procedure. The Pocklington equation is solved via the Galerkin-Bubnov Inirect Boundary Element Method (GB-IBEM). An illustrative computational example is given, as well.