Oxide interfaces provide very intriguing phenomena, in particular a 2D electron gas (2DEG) emerging between robustly insulating perovskites. The 2DEG was detected in 2004 beneath polar LaAlO₃ (LAO) epitaxially grown on TiO₂-terminated SrTiO₃ (001) (STO). Herein, recent first-principles studies of 2DEGs are reviewed. Using a Green function method, the family of the polar/nonpolar (001) interfaces: LAO/STO, LaFeO₃/STO, and STO/KTaO₃ is computed. In the context of 2DEG, one of two insulating perovskites, at least, must be polar. The effect of a polar/polar interface is modeled for LAO/KTaO3(001) and also for the (110) and (111) interfaces of LAO/STO. Starting from the defectless superlattice with its two differently terminated interfaces, we demonstrate that the 2DEG and 2D hole gas appear there, respectively, due to the presence of excessive electrons or holes. 2DEG is evaluated by its layer-resolved density profile along [001], as well as the Fermi surface cross sections and effective masses, which are directly related to the transport properties. The effects of intermixed cations, their vacancies, and oxygen vacancies at each interface of LAO/STO are calculated. Finally, we show how to tune reversibly the 2DEG by changing the electronic balance at the LAO surface that mimics the effect of ionic liquid gating.