The success of TCAD depends on the reliability and efficiency of the computer models used. Due to the rapid progress of Si technology and the introduction of new device types and materials, known models are continuously being improved and new models are being developed. During this development process it is important to compare the results of TCAD simulations to those obtained by more fundamental methods. Here the Monte Carlo (MC) approach, in which the movement of electrons or holes within a material of interest is sampled over a simulation time period, proves to be very successful. As computational power increases, MC methods can even be used in combination with TCAD device simulations, helping to solve hot carrier and short channel problems. Basically there are two representations of the band structure of a material in an MC simulator: namely, analytical expressions, such as the parabolic or non-parabolic approximations, or a fullband structure. In the latter case the band structure is calculated in a part of the first Brillouin zone - the so-called irreducible wedge - and then passed to the MC simulator in the form of a three-dimensional mesh. Despite the higher computational costs, it is necessary to use the fullband approach for hot carrier problems, because an accurate representation of the band structure at higher energies is essential here. In contrast to hot electrons, cold electrons are located in a small area around the valley minima most of the time. The use of a refined, unstructured mesh with high resolution around the valley minima provides accurate results even in the combined low temperature - low field regime. Newest developments include the fullband MC simulation of carrier transport for arbritrary stress/strain conditions. To calculate the fullband structures, the empirical pseudopotential method (EPM) is generalized. Simulation results for hole transport in uniaxially stressed germanium have shown, that very high mobility gains can be obtained by stress engineering.