In 1905, by demonstrating the photoelectric effect, Albert Einstein showed that light (which has been thought of as a form of electromagnetic waves), must also be thought of as localized in packets of discrete energy.  In 1924, Louis-Victor Broglie propsed that electrons have wave properties, an example being wavelength and frequency; their wavelike nature was experimentally established in 1927 by the demonstration of their diffraction.  The theory of quantum electrodynamics combines the wave theory and the particle theory of electromagnetic radiation.