Today, Maxwell’s equations are exactly 140 years old, and it seems that we have already revealed all there is to know about them. But do we? What new and beautiful physics is still hidden in them? Can a beam bend itself to steep angles, maybe even more than 90°? We have recently addressed this challenge, and found the full vector solutions of Maxwell’s equations for shape-preserving accelerating beams. Subsequently, we tackled many other challenges where shaping light creates complex and novel phenomena.