We consider parallel plane (pp) waves, solutions of Einstein’s equations for which the linearized equation is exact. We describe the Penrose theorem, for the Penrose limit, saying that in the neighborhood of a null geodesic, any space looks like a pp wave. We exemplify it for AdS3 × S3. We then consider gravitational shockwaves, an example of pp waves, in flat space, and in other backgrounds. Finally, we describe the Khan–Penrose interacting solution, for the head-on collision of two gravitational shockwaves.