Jets at high energies, factorization and jet vertex in NL ln(s)

The next-to-leading corrections to the jet vertex which is relevant for the Mueller-Navelet jets production in hadronic collisions and for the forward jet cross section in lepton-hadron collisions are presented in the context of a k_t factorizazion formula which resums the leading and next-to-leading logarithms of the energy. Both the quark- and gluon-initiated contribution are now computed. This completes the framework for a full phenomenological analysis of Mueller-Navelet jets in NL log(s) approximation. Forward jets phenomenology still requires the NL photon impact factor.