The classical trajectory methodology for studying scattering of ions, atoms, or molecules from ice surfaces, and photodissociation of water at or in the surface of ice, is presented. The forces between the collider and the water molecules, or between the fragments of a dissociating molecule and the surrounding water molecules, are based on pair potentials taken either from ab initio calculations or derived empirically. Dynamical observables like sticking probabilities and kinetic energy distributions of desorbing photo-fragments are computed by solving Newton's equations of motion, starting from representative initial conditions. Four studies with relevance to astrochemistry are considered: the sticking of H atoms to ice Ih, the sticking of CO to ice Ih and ice Ia, the sticking of protons to ice Ih, and the photodissociation of water in ice Ih and ice Ia, also with a view to the subsequent chemistry of the H-and OH-products with co-adsorbed molecules. Where possible, the theoretical results are compared with experiments.