In the past three decades there has been enormous progressin identifying the essential role that nonlinearity playsin physical systems, including supporting soliton-likesolutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress hasoccurred in understanding the effects of disorder in linearquantum problems, especially regarding Anderson localizationarising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise andnonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to developsystematic techniques which can include all of theseingredients, which may reinforce, complement or frustrateeach other. This book contains a range of articles whichprovide important steps toward the goal of systematicunderstanding and classification of phenomenology. Experts from Australia, Europe, Japan, USA, and the USSRdescribe both mathematical and numerical techniques -especially from soliton and statistical physics disciplines- and applicaations to a number of important physicalsystems and devices, including optical and electronictransmission lines, liquid crystals, biophysics andmagnetism.