We review and discuss the first fully three-dimensional study of non-equilibrium carrier dynamics governing semiconductor-based intersubband optoelectronic devices, such as quantum-cascade lasers. First, a multisubband Monte Carlo simulation scheme in a kinetic Boltzmann-like approach is presented. Then, its generalization into a density-matrix quantum-transport formalism is discussed. This allows us to directly access microscopic key features of the electron relaxation dynamics (without resorting to phenomenological parameters) as well as to investigate the nature, coherent versus incoherent, of charge injection/transport processes. Applications to state-of-the-art mid-infrared quantum-cascade lasers and novel far-infrared emitters are reviewed. The extremely good agreement between theoretical results and experimental findings demonstrates that our approach is a valid and predictive tool for the understanding of charge transport in these quantum devices.