Electromagnetic radiation involves the oscillation of electric and magnetic fields at the same time. This principle applies to all forms of radiation.
When waves travel back and forth in a medium, they form a standing wave as a result of interference effects between the two halves of the wave.
Waves interact through interference, and this interference can result in waves either cancelling each other out or joining to make a bigger wave.
Diffraction is an interference effect seen when waves encounter a regular array. Diffraction demonstrates the wave-like nature of whatever is diffracted.
When light passes through a grating, it behaves as a wave. Longer wavelength light diffracts through a greater angle than shorter wavelength light.
In 1912, Max von Laue began investigating the use of a crystal of zinc sulfide to diffract X-rays, thus revealing any regular, repeated structure it might have.
X-ray crystallography depends on the analysis of diffraction effects from arrays of atoms in a crystal acting like the lines in a diffraction grating.
Clinton Davisson demonstrated electron diffraction, showing that electrons can sometimes be treated as waves. This property is used in the electron microscope.
A wave may be represented as a longitudinal wave or as a transverse wave, depending on which is most convenient for understanding it or making predictions.
Light is most easily considered as a wave, but it arrives in small packets known as photons. There is no single simple view fitting all the observed facts.
Light can be thought of as a wave or as a particle, depending on what we look for: this is called wave-particle duality. Sometimes we speak of 'wavicles'.
Discussing 'Newton's rings', Thomas Young pointed out that light appeared to be capable of destructively interfering with itself, clearly a wave phenomenon.