Anderson localization of surface plasmons in random metal-dielectric composites near the percolation threshold has been predicted and observed using scanning near-field optical microscopy. A scaling theory of local-field distributions and optical nonlinearities is developed. The theory predicts that the local fields are very inhomogeneous and consist of sharp peaks representing localized surface plasmons (sp). The localization maps the Anderson localization problem described by the random Hamiltonian with both on- and off-diagonal disorder. The local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of various optical phenomena. The white-light generation dramatically enhanced by the localized sp has been experimentally obtained. A feasibility of nonlinear single-molecule spectroscopy in percolation films has been shown.