In this talk, we shall introduce the notions of localized resonances. Usually these problems are related to the spectral of the Neumann-Poincare operators in different models. As an example, we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electro-magnetic fields, which are uniformly valid with respect to the nanoparticle’s bulk electron relaxation rate. Then, we discuss the scattering and absorption enhancements by plasmon resonant nanoparticles. Finally, we show the applications of localized resonance in imaging and cloaking.