The potential energy curves, spectroscopic constants, and low-lying vibration–rotation levels of ground-state O2 and its cation O+2 and anion O?2 were calculated with the explicitly correlated multireference configuration interaction method. The zeroth-order reference wavefunction was treated with the complete active space multiconfigurational self-consistent field method, in which the active space was carefully selected, and an additional molecular orbital πu was added into the full valence active space. The electron correlation of the 1s core in the oxygen atom was considered in the computations. The Davidson correction on molecular energy was considered to account for higher electron excitation. The relativistic effects, including the scalar relativistic effect and spin–orbit coupling, were considered in the computation of potential energy curves. These physical effects on the spectroscopic constants were examined. The low-lying levels of vibration–rotation spectra of O2 and its ions were determined based on the computed potential energy curves. Comparisons with available experiments were made and excellent agreement was obtained for the vibrational and rotational parameters. The spectroscopic constants and vibration–rotation spectrum of O?2 , which is sparse in experiments, were provided. Our study will shed some light on further theoretical and experimental studies on these simple but important molecular systems.