Virtual Element methods (VEM) are an extension of finite element methods to polytopal meshes. The basis functions of the underlying discrete space are not known in closed form since they are solutions to local PDEs. As a consequence, their explicit evaluation is not necessary and several quantities are not computed exactly. For instance: bilinear forms are constructed by means of polynomial projections plus stabilization terms handling the non-polynomial contribution to the discrete space, only a polynomial projection of the discrete solution is usually post-processed. In general, the stabilization term of the bilinear form only needs to scale as the original non-polynomial contribution, without satisfying any approximation property. Nevertheless, in some situations, the ``artificial'' nature of such term may pollute the results: this is the case, for instance, of anisotropic problems and eigenvalue problems. We present a Reduced Basis approach to VEM for efficiently solving the PDE associated to each virtual basis function [1,2]. Such method defines a new conforming space, the rbVEM space, satisfying optimal convergence properties and overcoming the VEM limitations we mentioned above. Next, we provide a brief overview of the application of rbVEM to second-order diffusion equations and the Laplace eigenvalue problem. This talk is based on projects in collaboration with: Silvia Bertoluzza (IMATI--CNR Pavia, Italy), Francesca Gardini (Universita` di Pavia, Italy), and Daniele Prada (IMATI--CNR Pavia, Italy). [1] F. Credali, S. Bertoluzza, D. Prada. Reduced basis stabilization and post-processing for the virtual element method. Computer Methods in Applied Mechanics and Engineering, 420, 116693. (2024). arXiv:2310.00625 [math.NA] [2] S. Bertoluzza, F. Credali, F. Gardini. {Avoiding stabilization terms in virtual elements for eigenvalue problems: the Reduced Basis Virtual Element Method}. In preparation.