It has been a long standing problem in astrochemistry to explain how molecules can form in a highly dilute environment such as the interstellar medium. In the last decennium more and more evidence has been found that the observed mix of small and complex, stable and highly transient species in space is the cumulative result of gas phase and solid state reactions as well as gas-grain interactions. Solid state reactions on icy dust grains are specifically found to play an important role in the formation of the more complex “organic” compounds. In order to investigate the underlying physical and chemical processes detailed laboratory based experiments are needed that simulate surface reactions triggered by processes as different as thermal heating, photon (UV) irradiation and particle (atom, cosmic ray, electron) bombardment of interstellar ice analogues. Here, some of the latest research performed in the Sackler Laboratory for Astrophysics in Leiden, the Netherlands is reviewed. The focus is on hydrogenation, i.e., H-atom addition reactions and vacuum ultraviolet irradiation of interstellar ice analogues at astronomically relevant temperatures. It is shown that solid state processes are crucial in the chemical evolution of the interstellar medium, providing pathways towards molecular complexity in space.