Matter-wave physics is inspired by the wave-particle duality of light that has intrigued scientists for more than 200 years by now. Already then it had been a matter of debate, for instance between Newton and Huygens, whether light needs to be understood as composed of particles or rather be propagating like waves.
This question was temporarily settled by the famous double slit experiment, performed by T. Young in 1908 : Propagation of light through an opaque screen with two open slits can only be explained when we assume that the light "knows" about the open/closed status of both slits.
While this appears not too surprising, as we also see wave phenomena in water waves or acoustics, it became a puzzle again with the insight that during its interaction with matter, light appears with localized momentum and energy - very much like a particle. This assumption is required to explain the photo effect - the light-induced ejection of electrons from a metal surface - and it also stimulated Einstein to propose the photon as a quantum of light .
In 1923 Louis de Broglie  proposed that every piece of matter must also be associated with a delocalized wave. Only four years later, this concept was verified by Davisson and Germer  who observed electron diffraction at a nickel surface, and by Thomson and Reid  using transmission through thin metal foils. Shortly later, in 1930, Estermann and Stern  reported the first diffraction of neutral helium beams and even molecular hydrogen at clean crystal surfaces. In 1936 neutron diffraction followed .
Meanwhile, electron diffraction has become a key tool in the materials sciences, in form of low-energy electron diffraction (LEED), electron holography or electron microscopy, where the short de Broglie wavelegths in the picometer range explains the high resolution that can be achieved. Also coherent neutron scattering has become a tool of everyday use in science: the 3D structure of condensed matter would be by far less well understood if it were not for the quantum wave nature of neutrons scattered at crystal lattices.
Double- and multi-slit diffraction experiments with massive matter have been realized with electrons , neutrons , atoms [10,11], small and cold  as well as large and hot molecules .
Over the years atom interferometry has been developed into at sophisticated tool for inertial force sensing in fundamental tests of general relativity as well as for applications as diverse as navigation and geodesy [14,15].
Macromolecule interferometry is still a young field of research, developed at the University of Vienna, with applications ranging from advances tests of fundamental quantum principles  to molecule metrology for physical chemistry and biomolecular physics [15,17].