This article presents a detailed discussion of the problem of the localization and various methods of describing it on the basis of plane waves multiply scattered in randomly layered media. It is noted that the field of localized waves has a complicated structure, with sharp peaks and extended ``dark'' regions, where the intensity of the wave is small. It is shown that because of this complicated structure the wave field in a randomly layered medium, the dynamic and statistical characteristics of the wave behave in fundamentally different ways. For example, the statistical moments of the intensity of the wave increase exponentially into the interior of the medium, while the energy of the wave penetrating into randomly inhomogeneous medium can be finite with unity probability. The concept of a majorant curve and of an isoprobability curve, helpful for understanding the phenomenon of localization, are introduced. Also taken into account is the effect of a small regular absorption on the statistical and dynamic properties of the wave, and the localization of space-time pulses in a randomly layered medium is also studied.