  The Balitsky-Kovchegov equation describes the high-energy growth of gauge
theory scattering amplitudes as well as nonlinear saturation effects which stop
it. We obtain the three-loop corrections to this equation in planar
$\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently
established equivalence with the physics of soft wide-angle radiation,
so-called non-global logarithms, and thus yields at the same time the
three-loop evolution equation for non-global logarithms. As a by-product of our
analysis, we develop a Lorentz-covariant method to subtract infrared and
collinear divergences in cross-section calculations in the planar limit. We
compare our result in the linear regime with a recent prediction for the
so-called Pomeron trajectory, and compare its collinear limit with predictions
from the spectrum of twist-two operators.
