The realm of the dynamics of bouncing droplets is a rather recent development in physics and mathematics. Just over a decade old, it holds many exciting avenues of exploration. In this thesis, I will present my research on millimetric liquid droplets, which walk across the surface of a vibrating fluid bath through a resonant interaction with their own wave fields. These walking droplets, or 'walkers', exhibit several features previously thought to be peculiar to the microscopic, quantum realm. In particular, walkers in confined circular corrals exhibit a wave-like statistical behaviour similar to that of electrons inside quantum corrals. My results show that localised topological inhomogeneities in an elliptical corral may significantly diminish or enhance the resonance of specific modes of the cavity. This leads to a controlled mode induction and to resonant projection effects in the statistical behaviour of the walker, which resembles effects observed in quantum corrals.