Oxygen vacancies play a key role in providing a fertile environment for superconductivity to emerge in the Ba₂CuO₄ and Sr₂CuO₄ family of novel superconductors. However, there is considerable debate as to whether or not the vacancies reside in the CuO₂ plane or at the apical sites. Using state-of-the-art ab initio techniques, we systematically examine the energy landscape and electronic structure of oxygen vacancies in Ba₂CuO₄ and Sr₂CuO₄. A number of different configurations involving single and multiple vacancies are considered. Planar vacancies are found to yield lower energies, and materials with apical vacancies display exotic band structures. Finally, we will briefly connect our results to recent experiments.