Atomic samples with temperatures in the nanokelvin range, prepared by advanced methods of laser and evaporative cooling, offer unique opportunities to study a large variety of phenomena in complex quantum systems. The important degrees of freedom and parameters can be controlled in a way, not accessible to traditional quantum many-body systems. Both bosonic and fermionic atoms are available to create Bose-Einstein condensates, degenerate Fermi gases, and even quantum-degenerate mixtures. Optical traps allow the experimentalists to realize macroscopic traps, artificial crystals (“optical lattices”), and low-dimensional environments. The interaction can be magnetically tuned exploiting a resonance phenomenon, called “Feshbach resonance”. Based on this rich tool-box, many intriguing model systems can be experimentally studied with strong connections to different branches of physics. After a general introduction into the field, I will present a few examples based on research in Innsbruck, including new developments on strongly interacting Fermi gases and few-body “Efimov” states in Bose gases.