Optical materials which are artificially structured on a nanometer scale allow for a variety of fundamentally new optical phenomena, like materials with negative refractive index, optical cloaking, or imaging at deep sub-wavelength resolution. Also, functionality of conventional optical elements can be greatly enhanced by using nano-structured materials, e.g., for anti-reflection or polarizing coatings. We are developing, investigating and applying finite-element based rigorous simulation methods for accurately solving Maxwell’s equations on relatively large, 3D computational domains, including arbitrarily shaped structures. In various collaborations with experimental groups we have been using our methods to design experimental setups and to analyze experimental findings. Also, the solvers have been transfered to several research groups worldwide.