It has long been recognized that the most interesting or active surfaces for the applications are not necessarily the most perfect ones. In insulating oxides, geometric defects, nanofacets, or stoichiometric defects are usually associated to specific electronic states located in the forbidden gap region, which confer a higher reactivity to the surfaces. From this view point, polar oxide surfaces are of prominent interest: their intrinsic instability, due to the existence of a non-zero dipole moment in the repeat unit perpendicular to the surface, may be overcome by a deep modification of the surface electronic structure --- total or partial filling of surface states, sometimes leading to surface metallization --- or by strong changes in the surface stoichiometry --- spontaneous desorption of atoms, faceting, large-cell reconstructions, etc. We will examine several of these issues, through the results of first principles simulations of the MgO(111) surface, based on the density functional method. We will discuss the relative stability of various surface reconstructions, in relation with recent grazing incidence X Ray diffraction and atomic force microscopy experiments. The mechanism by which is achieved the charge compensation necessary to heal the polarity when transition metal atoms are deposited on the surface will be described and the trends in the adhesion energy along the transition series will be discussed. Finally we will present recent results on the dissociation of water on MgO(111).