We introduce and develop two bipolar transport models which are based on appreciably different physical assumptions regarding the distribution function in the energy levels of trap states. In the first model, conduction is described by an effective mobility of the carriers and the accumulation of stored space charge is taken into account through a single trapping level. In the second model the hypothesis of an exponential distribution function of trap depth is made, with conduction taking place via a hopping process from site to site. The results of simulations of the two models are compared with experimental data for the external current and the space-time evolution of the electrical space charge distribution. The two descriptions are evaluated in a critical way, and the prospects for these models to adequately describe real systems are given.