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

High Energy Physics - Phenomenology