We describe the standard Foldy–Wouthuysen transformation technique along with its applications in optics and the new results it leads to. The use of the Foldy–Wouthuysen transformation technique is central in the non-traditional prescriptions of Helmholtz optics and Maxwell optics, respectively, resulting in the wavelength-dependent modifications of light beam optics, even at the paraxial level. It is further shown that the wavelength-dependent modifications in the newly developed formalisms of light beam optics are in close anology with the quantum theory of charged-particle beam optics.