  This tutorial review gives an overview of the transverse Anderson
localization of light in one and two transverse dimensions. A pedagogical
approach is followed throughout the presentation, where many aspects of
localization are illustrated by means of a few simple models. The tutorial
starts with some basic aspects of random matrix theory, and light propagation
through and reflection from a random stack of dielectric slabs. Transverse
Anderson localization of light in one- and two-dimensional coupled waveguide
arrays is subsequently established and discussed. Recent experimental
observations of localization and image transport in disordered optical fibers
are discussed. More advanced topics, such as hyper-transport in longitudinally
varying disordered waveguides, the impact of nonlinearity, and propagation of
partially coherent and quantum light, are also examined.
