The quantum framework of the time-dependent density functional theory (TDDFT) for analyzing nanostructured devices is reviewed, and alternative methods for incorporating induced electromagnetic fields into the theory are discussed. To capture the retardation effects in larger electronic structures, the TDDFT equations can be formulated by applying the Lorenz gauge-fixing condition to the induced scalar and vector potentials (analogous to macroscopic formulations used in antenna theory). Evaluating the retarded potentials via radiation integrals, however, rapidly becomes the computational bottleneck within the TDDFT time-marching framework if done in a brute-force manner. This article demonstrates that 3D space or 4D space-Time fast Fourier transform (FFT) schemes can be adopted to accelerate these computations and reduce the costs of evaluating the potentials below the typical computational bottleneck of TDDFT. Thus, FFT-Accelerated Lorenz gauge retarded potentials become an attractive candidate for replacing the conventionally used electrostatic-induced scalar potential within TDDFT.