Matter is discrete and complex. Physical phenomena are however often described by few equations with a small number of macroscopic variables. Our understanding of Nature therefore stems from simple classical and quantum models of the underlying  microscopic quantum world. The universality, accuracy and predictive power of these coarse grained models prompts fundamental questions:

• ​Which aspects of complex quantum systems allow for a simple effective description?
• How can we isolate the variables making the effective description of a quantum system simple and accurate?
• How can we exploit quantum phenomena to realize devices?

Quantum complexity deals with these fundamental questions.