Detailed laboratory studies and progress in surface science technique, have allowed in recent years the first experimental confirmation of surface reaction schemes, as introduced by Tielens, Hagen and Charnley [1,2]. In this paper, we review few heterogeneous processes which give routes to form elementary molecules considered as precursors for explaining the variety and richness of molecular species in the interstellar medium. Adsorption, diffusion and reaction processes are discussed. With emphasis on the experimental approaches, but also supported by theoretical developments, progresses in the understanding of the "catalytic role" of a dust grain surface in various physical conditions are described. Recent advances made on few important species (H2, H2O, CH3OH) are used to illustrate basic properties and raise open questions.@en