Electrons that carry the electric current in a metal wire, scatter from the defects of the crystalline structure of the metal and
traverse the wire by random walk. According to quantum mechanics, at low temperatures the electrons acquire wave
properties and are thus subject to interference effects that slow this random walk down and can even halt it completely. This is
Anderson localization discovered almost 70 years ago. In the 1980s, physicists realized that the same phenomenon should also
take place for classical waves and, in particular, for light in strongly disordered media. Several successful experimental
demonstrations have been achieved in low-dimensional systems, but Anderson localization of light in three-dimensional
disordered media remains elusive. Recent theoretical work suggests that profound fundamental reasons may underlie this
difficulty: the vector nature of electromagnetic waves allows for longitudinal optical fields that have no analogue for quantum
particles obeying Schrodinger equation. Understanding how longitudinal fields prevent Anderson localization also helps to
come up with proposals of the ways to overcome this difficulty. In particular, we discuss proposals of experiments involving
light scattering by impurities in a transparent solid matrix subject to a strong external magnetic field or by conducting, metal
porous structures. In both cases, quite accurate theoretical analyses indicate that Anderson localization should take place
under realistic experimental conditions, giving us hope for successful experimental realizations in the near future