The SFB/CRC 1375 NOA was chosen by the German Research Foundation (DFG) in a competitive scientific panel and solely based on excellence criteria. NOA investigates fundamental nonlinear optical processes in nanostructures and low-dimensional systems. In an interdisciplinary approach of physicists, chemists and material scientists, we theoretically and experimentally explore quantum phenomena of light-matter interaction such as light-induced tunneling of electrons through metallic nanogaps, higher harmonic generation and field-driven carrier acceleration in plasmonic nanostructures, atomic lattices and 2D-materials. We aim to design new subwavelength-scale materials with tailored nonlinearities at atomic precision, e.g. for optical switching, sensing and energy conversion.