The elastic amplitudes in QCD feature a universal asymptotic behaviour in the limit of large centre-of-mass energy and fixed transferred momentum. In this regime, the amplitudes are described by the exchange of a Reggeized gluon in the t-channel, whose propagator generates a power of the large logarithm of the scale ratio to each perturbative order. Such behaviour corresponds to the presence of a Regge pole in the amplitude in complex angular momentum space. Going beyond the Leading Logarithms (LLs), the amplitudes receive contributions also from Regge cuts. In particular, these terms enter the Next-to-Leading Logarithms (NLLs) of the imaginary part and the NNLL of the real part of the amplitudes. In this talk, I will review a framework, based on rapidity factorisation, to disentangle the contribution of the pole and the one of the cuts, order-by-order in perturbation theory. I will talk about the application of this method to predict the NNLLs of the real part of the elastic amplitudes up to four-loop order. Finally, I will discuss the first steps in the investigation of the high-energy limit of the amplitudes for inelastic processes.
