This paper reviews structure and properties of crystals related to quantum mechanics of nuclear motion. The basic quantum theory of the harmonic oscillator and free rotor formed by atoms in molecules is briefly reviewed. It is extended to include tunnel states as explicit indication of the wave-like property of the nucleus. The term proton cloud is introduced to describe the delocalized proton. Deuteration-induced phase transitions in bromohydroxyphenalenone is presented as evidence for the quantum nature of the nuclear motion. Direct observation of the tunnel level by far infrared spectroscopy is described along with the potential energy curve for the proton derived from the spectroscopic data. Isotope-dependent properties are further reviewed for deuteration induced phase transitions in tri-alkali hydrogen disulfates and similar diselenates studied by calorimetry and neutron diffraction. Neutron diffraction at low temperature shows a delocalized proton in ground state of these crystals. In chromous acid an even stronger isotope effect occurs and has been discussed in terms of the crystal structure of this particular compound. Rotational tunneling of ammonium ions and its consequences in the phase behavior and structure are then discussed for diammonium hexachloroplatinate and isomorphous cubic crystals. Neutron diffraction combined with the low temperature heat capacity has revealed that the hydrogen nuclei in these crystals are delocalized in tori of 0.8 angstrom in diameter which surround tetrahedrally the nitrogen atom at the center of the ammonium ion. Finally, the relation of the wave-like properties of nuclear motion to chemical reaction and proton polarizability is discussed.