Temporal Quantum Correlations and Hidden Variable Models Introduction Preliminary notions Noncontextuality inequalities from variable elimination Optimal tests for state independent contextuality Quantum bounds for temporal correlations Dimension witnesses Conclusions. . In this thesis the main approach to the characterization of the set of classical probabilities the correlation polytope approach is reviewed for different scenarios namely hidden variable models discussed by Bell (local) Kochen and Specker (non contextual) and Leggett and Garg (macrorealist). Computational difficulties associated with the method are described and a method to overcome them in several nontrivial cases is presented. For the quantum case a general method to analyze quantum correlations in the sequential measurement scenario is provided which allows computation of the maximal correlations. Such a method has a direct application for computation of maximal quantum violations of Leggett Garg inequalities and it is relevant in the analysis of non contextuality tests. Finally possible applications of the results for quantum information tasks are discussed.