ABX3 compounds with perovskite structure have been intensively and extensively studied in the last decades in view of their structural richness and amazing variety of interesting properties, such as piezoelectricity, ferroelectricity, ferromagnetism, superconductivity, magnetoresistance, multiferroicity, etc. In this chapter, we recompile well-established chemical and structural concepts in pure inorganic perovskites (mainly oxidic perovskites), and extend them to the young family of hybrid organic-inorganic perovskites. Our final goal is to help understanding the relationships among composition, crystal structure and properties in this new family of compounds, for inspiring further the design of novel materials.