We illustrate how our recent light-front approach simplifies relativistic electrodynamics with an electromagnetic (EM) field F µν that is the sum of a (even very intense) plane travelling wave F µν t (ct−z) and a static part F µν s (x, y, z); it adopts the light-like coordinate ξ = ct−z instead of time t as an independent variable. This can be applied to several cases of extreme acceleration, both in vacuum and in a cold diluted plasma hit by a very short and intense laser pulse (slingshot effect, plasma wave-breaking and laser wake-field acceleration, etc.)1. E, B are constant or vary "slowly" in space/time; 2. the motion of the particle keeps non-relativistic;3. E, B are so small that nonlinear effects in E, B are negligible;4. E, B are monochromatic waves, or very slow modulations thereof.