Technological progress has lead to a huge growth in the field of mesoscopic physics over the past decade, and buzzwords like spintronics or quantum computing have created much excitement. At the origin of this development is the ongoing miniaturization and the ever increasing control over systems at the nanoscale. Central elements in understanding mesoscopic systems are the reduced dimensionality as well as the interplay of interactions and disorder. Luttinger liquid theory has been very successful in describing the low-energy properties of clean onedimensional systems. With the advent of more and more precise measurements, the question as to the limitations of Luttinger liquid physics has arisen only fairly recently. The proposed research explores (quasi-)onedimensional physics beyond the Luttinger liquid description, focusing on deviations from onedimensionality in interacting quantum wires and the interplay of interactions and disorder. Hybrid systems offer new ways of designing system functionality by combining materials with different, even antagonistic properties. A prime example are superconductor-ferromagnet systems where the incompatibility of the spin properties leads to a number of unusual phenomena. The proposed research explores correlations and dynamic (spin) effects in hybrid systems. Finally, ultracold atomic systems have opened a new window on interacting quantum systems. Since the first realization of Bose-Einstein condensation of a gas of bosonic atoms, ultracold atom physics has rapidly evolved. Pairing of fermions has been observed with the analogue of two spin states realized using two different hyperfine states. One of the most exciting features of these recently discovered atomic paired-fermion superfluids is the tunability of the interactions via a magnetic field-induced Feshbach resonance. The proposal considers ultracold gases in an inhomogeneous magnetic field to explore aspects of (quasi-)onedimensional and hybrid systems.