We review recent theoretical advances in the modeling and computer simulation of complex non-linear spatio- temporal dynamics of charge carriers in semiconductors. Among the particularly instructive examples are investigations of current filaments in doped semiconductors in the regime of low temperature impurity breakdown. The nascence of current filaments in thin GaAs films with different contact geometries, including circular samples (Corbino disks) with symmetry breaking instabilities, is investigated, and the role of global couplings induced by the operating load circuit is analysed.