The chemical and electronic properties of copper combined with its large natural abundance lend this material to impact a wide range of technological applications, including heterogeneous catalysis. The reactivity of copper in its Cu¹⁺oxidation state makes this specific configuration relevant in various chemical reactions, but the facile redox properties of copper make the isolation of individual states for fundamental studies difficult. Here we review three Cu₂O model systems used to study the interaction of Cu¹⁺ with small molecules making use of surface science techniques: Cu₂O/Cu(111), thin polycrystalline Cu₂O films on Cu foil, and bulk Cu₂O crystals. Advantages and disadvantages of each system are discussed and exemplified through case studies of chemical adsorption and reactivity studies.