The structural, energetic, and electronic properties of stoichiometric and defective Li2O were studied theoretically. The reliability of the Perdew-Wang method in the framework of density functional theory (DFT), and of two DFT/Hartree-Fock hybrid methods (PW1PW and B3LYP), was examined by comparison of calculated and available experimental data. Atom-centered orbitals and plane waves were used as basis functions for the crystalline orbitals. For both cases, the basis set dependence of calculated properties was investigated. With most of the methods, good agreement with the experimental Li2O lattice parameter and cohesive energy was obtained. In accordance with experiment, the analysis of electronic properties shows that Li2O is a wide gap insulator. Among the considered methods, the hybrid methods PW1PW and B3LYP give the best agreement with experiment for the band gap. The formation of an isolated cation vacancy defect and an F center in Li2O were studied. The effect of local relaxation on the calculated defect formation energies and the defect-induced changes of electronic properties were investigated and compared to available experimental results. The migration of a Li+ ion in Li2O bulk was investigated. The activation energy for the migration of a Li+ ion from its regular tetrahedral site to an adjacent cation vacancy was calculated, including the effect of local relaxation. The calculated activation barriers, 0.27-0.33 eV, are in excellent agreement with experiment.