Periodic structures with a sub-wavelength pitch have been known since Hertz conducted his first experiments on the polarization of electromagnetic waves. While the use of these structures in waveguide optics was proposed in the 1990s, it has been with the more recent developments of silicon photonics and high-precision lithography techniques that sub-wavelength structures have found widespread application in the field of photonics. This review first provides an introduction to the physics of sub-wavelength structures. An overview of the applications of sub-wavelength structures is then given including: anti-reflective coatings, polarization rotators, high-efficiency fiber-chip couplers, spectrometers, high-reflectivity mirrors, athermal waveguides, multimode interference couplers, and dispersion engineered, ultra-broadband waveguide couplers among others. Particular attention is paid to providing insight into the design strategies for these devices. The concluding remarks provide an outlook on the future development of sub-wavelength structures and their impact in photonics.