The calcium copper titanate CaCu3Ti4O12 is a distorted perovskite exhibiting a giant dielectric constant with non-ferroelectric temperature behavior. Recent investigations tend to attribute the origin of the anomalous behavior of CaCu3Ti4O12 dielectric properties to the presence of heterogeneous microstructure and grain boundary layers, excluding that the giant dielectric constant is present in perfectly stoichiometric, defect-free crystals. The intrinsic origin is also ruled out by the normal dielectric behavior obtained in ab initio Density Functional Theory (DFT) calculations. In this work, we present ab initio calculations performed to estimate the energies associated with the creation of defects in the CaCu3Ti4O12 lattice, including oxygen and copper vacancies, and investigate their electronic properties. Furthermore, with a view at ascertaining whether correlation effects may modify the electronic structure and dielectricity of CaCu3Ti4O12, we present an application to CaCu3Ti4O12 of a DFT-based pseudo-selfinteraction-correction (pSIC) method already applied successfully to Mott insulators.