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We review recent progress on the calculation of scattering amplitudes in thehigh-energy limit. We start by illustrating the shockwave formalism, whichallows one to calculate amplitudes as iterated solutions of rapidity evolutionequations. We then focus on our recent results regarding $2\to 2$ partonscattering. We present the calculation of the imaginary part of the amplitude,at next-to-leading logarithmic accuracy in the high-energy logarithms, formallyto all orders, and in practice to 13 loops. We then discuss the computation ofthe real part of the amplitude at next-to-next-to-leading logarithmic accuracyand through four loops. Both computations are carried in full colour, andprovide new insight into the analytic structure of scattering amplitudes andtheir infrared singularity structure.

Two-parton scattering in the high-energy limit: climbing two- and three-Reggeon ladders