Recent studies of charge trapping and charge transport in spolymer films irradiated and charged with monoenergetic electrons of range smaller than the sample thickness and thereafter stored or annealed under various conditions are discussed. An analytical model used to describe the phenomena takes the following parameters into consideration: Charge and energy deposition profiles, charge drift due to a shallow-trap-modulated mobility, deep trapping without release, trap filling due to a finite trap density, and ohmic relaxation due to a radiation-induced conductivity during irradiation and its delayed component after irradiation. The model calculations show the effect of various parameters on the shape of the initial charge distribution and on its evolution with annealing time. - Experiments with the laser-induced pressure-pulse (LIPP) method on 12 and 25<FONT FACE="Symbol">m</font>m thick fluorocarbon and polymide films, charged with 10 or keV electron beams, respectively, yield the charge distributions after irradiation and the changes of the distributions due to annealing of the samples at 120oC for various times. A comparison of experimental and analytical results reveals the trapping kinetics and permits to estimate the deep-trap density and the <FONT FACE="Symbol">mt</font>-product, where <FONT FACE="Symbol">m</font> is the trap-modulated mobilit and <FONT FACE="Symbol">t</font> is the trapping time.