The authors expound the method of exact absorbing boundary conditions, which solves one of the most important theoretical problems in computational electrodynamics, namely, the problem of equivalent replacement of an open (with infinite domain of analysis) initial boundary value problem by a closed (with bounded computation domain) one. This method, being mathematically strict, allows proper formulation and numerical study of transient and steady-state processes in various open resonant systems. The authors present local (in space and time) and non-local exact absorbing conditions for virtual boundaries located in cross-sections of regular waveguides or in free space. The elaborated concept of the so-called virtual feeding waveguides allows to solve many practically interesting radiation problems. The approach outlined in this chapter was implemented in software for solving both scalar (plane and axially symmetric) and vector problems.