The Quantum Cascade Laser (QCL), first demonstrated in 1994, is at the verge of commercial application. Due to the incoherent nature of the stationary charge transport in QCL heterostructures, the time evolution of the carrier distribution function is governed by a semiclassical Pauli Master Equation (PME). To investigate charge transport in QCLs, a simulator has been developed which solves the PME by means of a Monte Carlo method. It includes relevant scattering mechanisms like electron-longitudinal optical phonon, acoustic and optical deformation potential, intervalley scattering, alloy scattering, and scattering due to rough interfaces. The electron states are evaluated within a self-consistent Schrödinger-Poisson solver. Given such carrier states, we consider the multi quantum well structure as a repetition of this periodicity region. The carrier transport is simulated over the central stage and every time a carrier proceeds an interstage scattering process, the electron is reinjected into the central region and the corresponding electron charge contributes to the current. A comparison of simulation results with measurements for a recently developed InGaAs/GaAsSb QCL has been carried out. The calculated and measured voltage-current characteristics are in acceptable agreement and deviations can be attributed to the non-optimized scattering parameters and to additional scattering mechanisms not yet available. It is possible to observe a dominant impact of polar optical phonon scattering and also significant effects due to alloy scattering. However, more remains to be done for future research. A large number of states are involved in transport, especially for THz QCLs. Subbands are close in energy and strongly coupled by Coulomb scattering, which can play an important role. For more precise simulations, a model for electron-electron scattering has to be added. Furthermore, the parameters of InGaAs based material systems are not well characterized, which requires careful attention.