We review the results of our studies on the production of two jets with a large interval of rapidity at hadron colliders, which was proposed by Mueller and Navelet as a possible test of the high energy dynamics of QCD, within the next-to-leading logarithm framework. The application of the BrodskyLepage-Mackenzie procedure to fix the renormalization scale leads to a very good description of the available CMS data at the LHC for the azimuthal correlations of the jets. We show that the inclusion of next-to-leading order corrections to the jet vertex significantly reduces the importance of energymomentum non-conservation which is inherent to the BFKL approach, for an asymmetric jet configuration.