Various processes that participate in ion beam surface modification are studied using phenomenological, analytical and first principle models. The processes that are modelled phenomenologically include preferential sputtering, radiation-damage induced migration and second phase precipitation. The models are based on numerical solutions of the transport equation and include the processes of ion collection, sputtering, lattice dilation or accommodation and diffusion as well. The model for preferential sputtering takes into account the depletion of the preferentially sputtered element at the surface and the atomic transport process that results from the concentration gradients caused by the depletion. Results are presented for the case of Ta implantation into Fe. ln the radiation-damage induced migration the flux of the solute atoms is coupled to the concentration gradient of the continuously introduced defects. Examples of implantation of Sn into Fe and N into Fe are modeled to demonstrate the influence of radiation-damage induced migration. The precipitation of second phases during irradiation is modelled using thermodynamic considerations but with solubility values under irradiation obtained from experiment. In the model the solute atoms in excess of the solubility limit are assumed to precipitate out. Calculations are presented for the case of N implantation into Nb. Using first principle calculation for binary collisions in solids a computer simulation code was developed to study the collisional mixing occurring during high fluence ion implantation. It is based on the Monte Carlo code TRIM, and is capable of updating the target composition as the implantation process proceeds to high fluences. The physical basis for the dynamic simulation as well as a detailed analysis on the statistics required for obtaining the profiles with a given accuracy are presented. Vectorized results in a high computational efficiency. The predicted collisional broadening of the implantation profiles is presented for Ar bombardment into a Sn-Fe target as well as Ti implantation into C-Fe. The results are compared to those of the diffusion approximation. A semi-empiricaI model based on an analytical evaluation of ion mixing at low temperatures was developed taking into account collisional mixing and thermal spike effects, as well as the thermal spike shape. The ion beam mixing parameter for the thermal spike is derived as being proportional to different powers of the damage parameter, i.e. the damage energy scaled by the cohesive energy of the matrix, dependent on the thermal spike shape and point defect density in the thermal spike regions. Three different regions of ion beam induced mixing were recognized according to different density levels of the damage parameter. An experiment was conducted to determine the effect of chemical or thermodynamic factors in the migration of C in the presence of Fe and Ti atoms. A marker layer of C in a Fe-Ti matrix was ion beam mixed using Ar. The large mixing effect is tentatively attributed to a favorable heat of mixing values. / Ph. D.