The recent developments in laser cooling, together with a preceding decade of work on cryogenically cooled atomic hydrogen, have opened possibilities for a large variety of experiments in which collisions between very slow atoms play an important role. Examples of such experiments are reviewed with an emphasis on theoretical interpretation. We focus primarily on open problems in this field and on subjects not yet dealt with in the existing reviews. Most of the examples deal with collisions between ground state atoms. Although a future development is foreseen in the direction of longitudinally cooled and bright beams, all present examples deal with experiments on gas samples. In that connection some attention is devoted to the step required to go from a microscopic to a macroscopic description.