We show that the reflection of quantum-mechanical waves from semiconductor surfaces creates new regimes of nonlinear dynamics, which offer sensitive control of electrons and ultra-cold atoms. For electrons in superlattices, comprising alternating layers of different semiconductor materials, multiple reflections of electron waves from the layer interfaces induce a unique type of chaotic electron motion when a bias voltage and tilted magnetic field are applied. Changing the field parameters switches the chaos on and off abruptly, thus producing a sharp increase in the measured current flow by creating unbounded electron orbits. These orbits correspond to either intricate web patterns or attractors in phase space depending on the electron decoherence rate. We show that related dynamics provide a mechanism for controlling the transmission of electromagnetic waves through spatially-modulated photonic crystals. Finally, we consider the quantum dynamics of a Bose-Einstein condensate, comprising 120,000 rubidium atoms cooled to 10 nK, incident on a stadium billiard etched in a room-temperature silicon surface. Despite the huge temperature difference between the condensate and the billiard, quantum-mechanical reflection can shield the cold atoms from the disruptive influence of the surface, thus enabling the billiard to imprint signatures of single-particle classical trajectories in the collective motion of the reflected atom cloud.