This Thesis focuses on the combination of reduced order models and data-driven techniques applied to the study of turbulent flows in order to improve the pressure and velocity accuracy of standard reduced order methods. The full order model is based on the incompressible Navier-Stokes equations; the reduced order model is constructed by means of Proper Orthogonal Decomposition with Galerkin approach. The available data are used to construct different correction/closure terms, which are added to the reduced equations in order to model the interaction between the resolved and the unresolved scales. Both supremizer enrichment approach and Poisson equation approach have been considered for pressure treatment at the reduced level.