Using both standard and explicitly correlated ab initio methods in conjunction with several atomic basis sets, the ground state of AlO(X 2 Σ + ) and the two lowest electronic states of AlO + ( 1 Σ + and 3 Π) are investigated. Potential energy curves for these species are mapped, which are incorporated later to solve the nuclear motion problem. Benchmark computations on AlO(X 2 Σ + ) are used to determine the reliability of the theoretical methods and basis sets used for an accurate description of aluminum oxide compounds. The electronic ground state of AlO + is X 1 Σ + , followed by the low-lying 1 3 Π state. For both cationic electronic states, a set of spectroscopic parameters are recommended that may help in the identification of this ion in laboratory and astrophysical media. An accurate estimation of the adiabatic ionization energy of AlO, AIE = 9.70 eV, is also reported.