The concept of quantum beams unifies a multitude of different kinds of radiation that can be considered as both waves and particles, according to the quantum mechanical model. Examples include light, in the form of X-rays and synchrotron radiation, as well as neutrons, electrons, positrons, muons, protons, ions, and photons. While the past century saw the discovery of these types of radiation and particles along with the investigations of their physical properties and their fundamental interaction with matter, the current century focuses extensively on their applications to characterize and understand materials in their broadest context, under all imaginable conditions. X-rays diffract to deliver crystal structures, while muons probe for the local magnetism in such crystals. Similarly, neutrons diffract and probe for magnetism, while both γ-rays and positrons allow to measure the electronic density of states; or again X-ray, neutron or electron diffraction probes for crystal defects in addition to ion beam channeling. Because of their penetration, X-rays, neutrons and muons can be used for imaging, such as radiography and tomography. At the same time, the types of quantum beams are different in which information can be obtained when investigating a particular material. Take the difference in cross-sections between neutrons and X-rays, respectively emphasizing the light or the heavy elements in a compound or alloy. While neutrons diffract from nuclei and, as elementary magnets via their spins, they allow determination of crystal and magnetic structure via crystallographic methods. Muons, on the other hand, can be embedded as interstitials into crystals, locally probing the site and its surrounding electromagnetic potential landscape. There is much interest in the dynamics of matter-how electricity and heat are transported through a crystal, related to inelastic scattering of quantum beams. Again, neutrons win overall for the investigation of phonons, while visual light scattering in the form of Raman spectroscopy is much easier to conduct and delivers complementary information.