A short overview of fundamental chemistry of lutetium and of structural characteristics of lutetium coordination complexes, as relevant for understanding the properties of lutetium-177 radiopharmaceuticals, is presented. This includes basic concepts on lutetium electronic structure, lanthanide contraction, coordination geometries, behavior in aqueous solution and thermodynamic stability. An illustration of the structure and binding properties of the most important chelating agents for the Lu(3+) ion in aqueous solution is also reported with specific focus on coordination complexes formed with linear and macrocyclic polydentate amino-carboxylate donor ligands.