Usually, scattering amplitudes in quantum field theory are computed perturbatively around a trivial background, but there are many reasons to be interested in non-trivial (or 'strong') background fields. These range from laser physics and QCD processes near heavy ion collisions to gravitational waves, conformal field theories and cosmology. Strong backgrounds also give us a way to test the robustness of new structures which have been discovered in scattering amplitudes. I will discuss perturbative Yang-Mills theory on a particularly simple (but important) background known as a plane wave, and consider a very basic observable: the scattering amplitude for a gluon to flip helicity as it crosses the background. This 'helicity flip' amplitude is a loop effect, and the leading result for Yang-Mills (and QCD) can be expressed compactly using a background-dressed version of the spinor helicity formalism (a method for freely specifying on-shell kinematics). Time permitting, I may also make some remarks about higher-point gluon amplitudes in the plane wave background, or the version of this story for gravity.