A reduced-density-matrix description is developed for coherent linear and non-linear electromagnetic interactions of quantized electronic systems in the presence of environmental decoherence and relaxation phenomena. Applications of interest include many-electron atomic systems and semiconductor materials. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified manner. The general non-Markovian formulations provide a rigorous foundation for the systematic introduction of the commonly used Born (lowest-order perturbation-theory) and Markov (short-memory-time) approximations. A preliminary semiclassical perturbation-theory treatment of the electromagnetic interaction is introduced, based on a coupled hierarchy of relationships for the field components of the reduced density operator.