A critical review is given on phenomenological models of damage accumulation used in binary collision (BC) computer simulations of the dose dependence of the shape of as-implanted profiles and of the interdependence of channeling and damage buildup The statistical approach, which assumes the accumulation of amorphous pockets, is found to be the most realistic model for doses below the amorphization threshold. The dynamic simulation of the formation of amorphous layers is described by an improved model. If within a certain depth interval the density of amorphous pockets exceeds a critical value, abrupt amorphization occurs. The model is applied in the Crystal TRIM code. Using only two empirical parameters, the change of the shape of range distributions with growing dose as well as the formation of amorphous layers during ion bombardment can be simulated. One parameter describes the accumulation of amorphous pockets and depends on the target temperature. The other parameter is independent of temperature and models the onset of amorphization. Results of Crystal-TRIM calculations for B+, BF2+, P+, and As+ implantations are compared with a comprehensive set of experimental data on range and damage profiles obtained by secondary ion mass spectroscopy, cross-sectional transmision electron microscopy, and channeling Rutherford backscattering spectroscopy. In general, good agreement between simulations and measurements is found.