  Using an iterative solution of rapidity evolution equations, we compute
partonic $2\to 2$ gauge theory amplitudes at four loops in full colour up to
the Next-to-Next-to-Leading Logarithms (NNLL) in the Regge limit. By
contrasting the resulting amplitude with the exponentiation properties of soft
singularities we determine the four-loop correction to the soft anomalous
dimension at this logarithmic accuracy, which universally holds in any gauge
theory. We find that the latter features quartic Casimir contributions beyond
those appearing in the cusp anomalous dimension. Finally, in the case of ${\cal
N}=4$ super Yang-Mills, we also determine the finite hard function at four
loops through NNLL in full colour.
