In this paper, the review of recent results of calculations of surface relaxations, energetics, and bonding properties for ABO3 perovskite (001), (011) and (111) surfaces using mostly a hybrid description of exchange and correlation is presented. Both AO and BO2-terminations of the nonpolar (001) surface and A, BO, and O terminations of the polar (011) surface, as well as B and AO3-terminations of the polar (111) surface were considered. On the AO-terminated (001) surface, all upper-layer A atoms relax inwards, while all second layer atoms relax outwards. For the BO2-terminated (001) surface, in most cases, the largest relaxations are on the second-layer metal atoms. For almost all ABO3 perovskites, the surface rumpling is much larger for the AO-terminated than for the BO2-terminated (001) surface, but their surface energies are always quite similar. In contrast, different terminations of the (011) ABO3 surface lead to very different surface energies for the O-terminated, A-terminated, and BO-terminated (011) surface, respectively. A considerable increase in the Ti–O or Zr–O, respectively, chemical bond covalency near the (011) surface as compared both to the bulk and to the (001) surface in ABO3 perovskites were predicted. According to the results of ab initio calculations for Nb doped SrTiO3, Nb is a shallow donor; six nearest O ions are slightly displaced outwards from the Nb ion. The F center in ABO3 perovskites resembles electron defects in the partially-covalent SiO2 crystal rather than usual F centers in ionic crystals like MgO and alkali halides. The results of calculations for several perovskite KNbxTa1-xO3 (KTN) solid solutions, as well as hole and electron polarons in ABO3 perovskites are analyzed.