A number of intriguing properties emerge upon the formation of the epitaxial interface between the insulating oxides LaAlO3 and SrTiO3. These properties, which include a quasi two-dimensional conducting electron gas, low temperature superconductivity, and magnetism, are not present in the bulk materials, generating a great deal of interest in the fundamental physics of their origins. While it is generally accepted that the novel behavior arises as a result of a combination of electronic and atomic reconstructions and growth-induced defects, the complex interplay between these effects remains unclear. In this report, we review the progress that has been made towards unraveling the complete picture of the SrTiO3/LaAlO3 interface, focusing primarily on present ab initio theoretical work and its relation to the experimental data. In the process, we highlight some key unresolved issues and discuss how they might be addressed by future experimental and theoretical studies.