We applied advanced ab initio treatments and large atomic basis sets to characterize the cesium oxide diatomic molecule (CsO) and its cation (CsO+) and anion (CsO-). We computed the electronic potential energy curves (PECs) of the low-energy states of these species along the internuclear distance to study their stability and spectroscopy. For these states, we computed vertical and adiabatic excitation energies and we found that those characterized as stable are mostly mono-configurational in nature. By solving the nuclear motion problem, we deduced a set of accurate spectroscopic data, including equilibrium geometries, harmonic vibrational frequencies, rotational constants, anharmonic vibrational constants, and the patterns of vibrational levels. Furthermore, we investigated the effect of the spin-orbit coupling on the electronic states correlating to the two lowest dissociation limits of the neutral molecule. We found that the PECs of these states are affected by the spin-orbit interaction. The adiabatic ionization energy of CsO is determined to be 6.52 eV. We compute also a relatively small adiabatic electronic affinity for CsO of 0.235 eV. Both values are in fair agreement with the experimental measurements. Our data may be used to identify CsO, CsO- and CsO+ in the laboratory or in oxygen- and cesium-rich media.