In this paper, the review of recent results of calculations of surface relaxations, energetics, and bonding properties for ABO 3 perovskite (001), (011) and (111) surfaces using mostly a hybrid description of exchange and correlation is presented. Both AO and BO 2-terminations of the nonpolar (001) surface and A , BO , and O terminations of the polar (011) surface, as well as B and AO 3-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 BO 2-terminated (001) surface, in most cases, the largest relaxations are on the second-layer metal atoms. For almost all ABO 3 perovskites, the surface rumpling is much larger for the AO -terminated than for the BO 2-terminated (001) surface, but their surface energies are always quite similar. In contrast, different terminations of the (011) ABO 3 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 ABO 3 perovskites were predicted. According to the results of ab initio calculations for Nb doped SrTiO 3, Nb is a shallow donor; six nearest O ions are slightly displaced outwards from the Nb ion. The F center in ABO 3 perovskites resembles electron defects in the partially-covalent SiO 2 crystal rather than usual F centers in ionic crystals like MgO and alkali halides. The results of calculations for several perovskite KNb x Ta 1-x O 3 (KTN) solid solutions, as well as hole and electron polarons in ABO 3 perovskites are analyzed.