This study describes the design and implementation of surrogate models for aerodynamic optimization or database generations. Two different methods are presented: the first one follows the classical methodology: a parametric POD is applied to a set of initial solutions or snapshots obtained with an high fidelity CFD model. With respect to approaches presented in literature, in this research work no truncation of the POD modes is performed and they are all used to construct the surrogate model. Several applications are presented: a backward facing step case, the analysis of the flow around a NACA 0012 airfoil and a RAE 2822 supercritical airfoil, the optimization of an automotive external shape and a database generation of a three-dimensional aircraft.