We investigate holographic complexity for eternal black hole backgrounds perturbed by shock waves, with both the complexity=action (CA) and complexity=volume (CV) proposals. We consider Vaidya geometries describing a thin shell of null fluid with arbitrary energy falling in from one of the boundaries of a two-sided AdS-Schwarzschild spacetime. We demonstrate how scrambling and chaos are imprinted in the complexity of formation and in the full time evolution of complexity via the switchback effect for light shocks, as well as analogous properties for heavy ones.