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Strong gravitational lensing is a phenomenon which occurs when the lines of sight to a foreground and background object nearly coincide, resulting in multiple imaging of the background object. Although quite rare, it offers an important diagnostic of masses and mass distributions in foreground objects ranging from stars to clusters of galaxies, and has the important advantage of being sensitive to all kinds of matter, both baryonic and dark. Strong lensing also gives magnified views of background objects, allowing easy study of otherwise inaccessible quantities, and potentially cosmological information owing to its sensitivity to combinations of mass density and lengths within the universe.

Quasars are relatively rare phenomena, and lensed quasars, in which a foreground galaxy provides the gravitational deflection in the right place, are correspondingly rare. However, they have some unique advantages: quasars allow easy access to the high redshift universe; quasars are bright, allowing easy study of subtle effects and potentially allowing complete samples to be built; quasars are variable, allowing cosmological information to be derived from time delays; quasars emit at multiple wavelengths, allowing detailed study of propagation effects. This review gives an overview of the history of quasar lensing, and a summary of its main applications. The applications fall into three parts: the use of quasars as probes of lens galaxies, both their stellar content via microlensing and their dark matter content via the fitting of models to lensed images; the use of quasar lenses to probe the structure and properties of the quasars themselves; and the use of quasar lenses for cosmology. A number of previous reviews have addressed some or all of these issues; see, for example Wambsganss (1998), Claeskens & Surdej (2002), Courbin, Saha & Schechter (2002), Kochanek & Schechter (2004), Kochanek (2004), Wambsganss (2004), Jackson (2007), Zackrisson & Riehm (2010), Bartelmann (2010), Schmidt & Wambsganss (2010). In this review individual theoretical results will be presented as needed, without derivation; the interested reader can refer to the standard text by Schneider, Ehlers & Falco (1992) for more detail. Finally I outline the possible future applications of quasar lensing, and the observational programmes which will develop the subject in the coming years.