I describe recent progress in understanding the high-energy limit in two-parton scattering in QCD, where towers of logarithms associated with Regge cuts have been compued. This was based on harnessing rapidity evolution equations to compute multi-Reggeon exchange contributions in both the real and imaginary parts of the amplitude. I show how the non-planar origin of Regge cuts, which menfests itself in the colour structure, helps to disentangle between the Regge pole and Regge cut and hence determine the Regge pole parameters to three loops.