A decade ago, Yves Couder and Emmanuel Fort discovered that droplets walking on a vibrating fluid bath exhibit several features previously thought to be exclusive to the microscopic, quantum realm. These walking droplets propel themselves by virtue of a resonant interaction with their own wavefield, and so represent the first realization of a macroscopic pilot-wave system. New theoretical developments provide rationale for the complex behavior of the bouncing droplets, and yield a trajectory equation for the walking droplets. Experimental and theoretical results in turn reveal and rationalize the emergence of quantization and wave-like statistics from pilot-wave dynamics in a number of settings. The relation between this hydrodynamic system and various realist models of quantum dynamics, including Louis de Broglie’s double-wave pilot-wave theory, is discussed, and would seem to invite a critical revisitation of quantum foundations.