We discuss fundamental optical phenomena at the interface of singular optics (“structured light”) and metamaterials (“structured media”), including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in optical metamaterials. The interaction of complex beams with nanostructured “engineered” media will bring new dimensions to the science and applications of complex light, including novel regimes of spin-orbit interaction, dispersion engineering, and nonlinear singular optics. We report theoretical and experimental studies of linear and nonlinear interactions of complex light beams with orbital angular momentum with fiber-based magnetic and negative-index metamaterials. Our initial theoretical studies predict that vortex-based nonlinear optical processes, such as second harmonic generation or parametric amplification that rely on phase matching, will also be strongly modified in negative index materials. These studies may find applications for multidimensional information encoding, secure communications, quantum cryptography using spin and orbital angular momentum, dispersion engineering for spontaneous param etric down-conversion, and on-chip optoelectronic signal processing.