The formation of molecules in the interstellar medium is an important topic of research nowadays because molecules play important roles in astrophysics and astrochemistry. Molecular hydrogen, the most abundant molecule, helps the cooling of collapsing clouds and through the study of its transitions, it gives information on the conditions of the ISM (Interstellar Medium) environment it finds itself in. While neutral or ionized, it intervenes in reactions to form most molecules that have been detected in the ISM. Water is the main component of ices coating dust grain; ices are the place of the formation and storage of molecules of biogenic interest. Furthermore, how water interacts with grains is of importance in understanding the delivery of water to planetary bodies. The formation of molecular hydrogen and water occurs largely on dust grains. Here we review the most important experimental discoveries about the formation of molecular hydrogen, and we present new work on the formation of water on ices and on grain analogs.