Given by Professor Charles Clark, Fellow of the Physical Measurement Laboratory at the National Institute of Standards and Technology, and Fellow and Adjunct Professor at the Joint Quantum Institute, University of Maryland, USA. Wave motions in nature were known to the ancients, and their mathematical expression in physics today is essentially the same as that first provided by d'Alembert and Euler in the mid-18th century. Yet it was only in the early 1990s that physicists managed to control a basic property of light waves: their capability of swirling around their own axis of propagation. During the past decade such techniques of control have also been developed for quantum particles: atoms, electrons and neutrons. I will present a simple description of these phenomena, emphasising the most basic aspects of wave and quantum particle motion. Neutron interferometry offers a poignant perspective on wave-particle duality: at the time one neutron is detected, the next neutron has not yet even been born. Here, indeed, each neutron "then only interferes with itself." Yet, using macroscopically-machined objects, we are able to twist neutron deBroglie waves with sub-nanometer wavelengths.