The interstellar medium is the matter that exists in the space between the star systems in a galaxy. It is composed of gas and elongated tiny dust grains. To date, plenty of molecules (> 170) are known to exist in the interstellar medium. The presence of most of them can be understood in terms of gas phase reactions but the synthesis of some key species (H2, H2O, CO2) need the intervention of solid-state reactions on dust grains surface. The aims of this thesis are to understand what are the relevant physical-chemical processes (i.e., diffusion and desorption) occurring on the surface of interstellar dust grains and how these processes influence synthesis of more and more complex molecules. In particular, the focus of my thesis is the inves...