It was in 'The Magellanic Cloud' (1955) -a science fiction novel by Stanislaw Lem -that engineers traveling to another star noticed that their spacecraft for unknown reasons overheated. The cause had to be outside the spaceship, but obviously there was only emptiness, at least compared to terrestrial conditions. The space between the stars, the interstellar medium, however, is not completely empty and at the high speed of the spacecraft the cross-section with impacting particles, even from such a dilute environment, was found to be sufficient to cause an overheating. Today, 60 years later, the interstellar medium has been studied in detail by astronomical observations, reproduced in dedicated laboratory experiments and simulated by complex astrochemical models. The space between the stars is, indeed, far from empty; it comprises gas, dust and ice and the molecules detected so far are both small (diatomics) and large (long carbon chains, PAHs and fullerenes), stable and reactive (radicals, ions, and excited molecules) evidencing an exotic and fascinating chemistry, taking place at low densities, low temperatures and experiencing intense radiation fields.Astrochemists explain the observed chemical complexity in space -so far 185 different molecules (not including isotopologues) have been identified -as the cumulative outcome of P a g e | 2 reactions in the gas phase and on icy dust grains. Gas phase models explain the observed abundances of a substantial part of the observed species, but fail to explain the number densities for stable molecules, as simple as water, methanol or acetonitrile -one of the most promising precursor species for the simplest amino acid glycine -as well as larger compounds such as glycolaldehyde, dimethylether and ethylene glycol. Evidence has been found that these and other complex species, including organic ones, form on icy dust grains that act as catalytic sites for molecule formation. It is here where particles 'accrete, meet, and greet' (i.e., freeze out, diffuse and react) upon energetic and non-energetic processing, such as irradiation by vacuum UV light, interaction with impacting particles (atoms, electrons and cosmic rays) or heating.This review paper summarizes the state-of-the-art in laboratory based interstellar ice chemistry. The focus is on atom addition reactions, illustrating how water, carbon dioxide and methanol can form in the solid state at astronomically relevant temperatures, and also the formation of more complex species such as hydroxylamine, an important prebiotic molecule, and glycolaldehyde, the smallest sugar, is discussed. These reactions are particularly relevant during the 'dark' ages of star and planet formation, i.e., when the role of UV light is restricted.A quantitative characterization of such processes is only possible through dedicated laboratory studies, i.e., under full control of a large set of parameters such as temperature, atom-flux, and ice morphology. The resulting numbers, physical and chemical constants, e.g., barrier heights, react...