In this talk, we present the development and analysis of a Mixed Virtual Element Method (Mixed -VEM) for the numerical approximation of eigenvalue problems arising from a general second-order elliptic operator. The mixed formulation naturally accommodates the approximation of both primal variables and fluxes, while the virtual element framework enables the use of general polytopal meshes without compromising stability or approximation properties. A rigorous a priori error analysis is carried out, providing convergence estimates for both eigenvalues and eigenfunctions. The analysis relies on suitable spectral approximation theory and highlights the consistency and stability of the mixed VEM discretization under standard regularity assumptions. Furthermore, we introduce a residual-based a posteriori error estimator specifically designed for the mixed VEM setting. The estimator is proven to be reliable and efficient and yields effective control of the error in the eigenfunction approximation, measured in appropriate norms. This estimator is particularly well suited for driving adaptive mesh refinement procedures aimed at enhancing the accuracy of the computed spectrum. A series of numerical experiments is presented to corroborate the theoretical results. The tests confirm optimal convergence rates, demonstrate the effectiveness of the proposed error estimator, and illustrate the robustness of the method on different mesh configurations. Overall, the proposed Mixed-VEM framework, combined with residual-type a posteriori error control, provides a flexible and accurate approach for the numerical approximation of second-order elliptic eigenvalue problems.