We discuss what happens to Anderson localization in a disordered lattice if nonlinearity is present. The situation is relevant for lattices of coupled oscillators, for a Bose-Einstein condensate (described by a nonlinear Gross-Pitaevsky equation) in a disordered potential, and to light propagation in a disordered nonlinear medium. Our main model is a discrete Anderson chain with a nonlinear term (nonlinear Schroedinger lattice with disorder). We discuss three problems:
i) How an initially localized wave packet spreads;
ii) How a regular wave is transmitted through a nonlinear disordered layer; and
iii) How a thermalization in a finite disordered lattice occurs.
In all cases nonlinearity leads to a weak chaos and delocalization