Oxygen vacancies have been shown to play a key role in the emergence of superconductivity in the recently discovered superconductor Ba₂CuO_4-δ. Interestingly, the amount of holes contributed by these vacancies is found to lie outside the typical superconducting dome of other cuprates. There is also considerable debate as to whether the vacancies reside in the CuO₂ plane or at the apical sites and what spatial configuration they occupy. Using state-of-the-art ab initio techniques, we systematically examine the energy landscape and electronic structure of oxygen vacancies in Ba₂CuO_4-δ. A number of different configurations involving single and multiple vacancies in apical and planar positions are considered. Planar vacancies are found to yield lower energies and display exotic band structures. Finally, we will briefly connect our results to recent experiments.