The invention of laser cooling methods for neutral atoms allows optical and magnetic trapping of cold atomic clouds in the temperature regime below 1mK. In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The extension of collision studies to the regime of optical lattices introduces several complicating factors. For the lattice studies, one has to account for the internal substates of atoms, position dependent matter-light coupling, and position dependent couplings between the atoms, in addition to the spontaneous decay of electronically excited atomic states. The developed one-dimensional quantum-mechanical model combines atomic cooling and collision dynamics in a single framework. The model is based on Monte Carlo wave-function simulations and is applied when the lattice-creating lasers have frequencies both below (reddetuned lattice) and above (blue-detuned lattice) the atomic resonance frequency. It turns out, that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position dependent light-matter coupling introduces selectivity of collision partners. The atoms, which are most mobile and energetic, are strongly favored to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. Consequently, the atoms remaining in the lattice have a smaller average kinetic energy per atom than in the case of non-interacting atoms. For bluedetuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. We find that the cooling and shielding dynamics do not mix and it is possible to achieve efficient shielding with a very simple arrangement. The simulations are computationally very demanding and would obviously benefit from the simplification schemes. We present some steps to this direction by showing how it is possible to calculate collision rates in near-resonant lattices in a fairly simple way. The method can then be used to combine quantum-mechanical and semiclassical models for cold collision studies in optical lattices.