Oxide electronics relies on the availability of epitaxial oxide thin films. The extreme flexibility of the chemical composition of ABO3 perovskites and the broad spectrum of properties they cover, inspire the creativity of scientists and place perovskites in the lead of functional materials for advanced technologies. Moreover, emerging properties are being discovered at interfaces between distinct perovskites that could not be anticipated on the basis of those of the adjacent epitaxial layers. All dreamed new prospects require the use of suitable substrates for epitaxial growth. Perovskite single crystals are the workhorses of this activity and understanding and controlling their surface properties have become critical. In this tutorial review we will chiefly focus on the impact of the morphology and composition of the surface of ABO3 perovskite substrates on the growth mechanisms and properties of thin films epitaxially grown on them. As SrTiO3 is the most popular substrate, we will mostly concentrate on describing the current understanding and achievements for it. Illustrative examples of other perovskite substrates (LaAlO3, LSAT and DyScO3) will be also included. We will show that distinct chemical terminations can exist on the surfaces used for growth and we will review methods employed either to select the most appropriate one for specific growth to allow, for instance, tailoring the ultimate outmost epilayer, or to induce self-ordering to engineer long-range nanoscale patterns of chemical terminations. We will demonstrate the capacity of this knowledge by the growth of low-dimensional organic and inorganic structures.