Emergence is central to our understanding of the world. It addresses the question of how did a seemingly unlimited diversity emerge from a small number of simple constituents. Ultimately emergence in physics is related to an inaccessibility of knowledge about the microscopic world, out of which new phenomena are formed at a larger scale. In quantum physics the Renormalization Group is a prominent example relating microscopic physics to emerging new phenomena. The main thrust in the research proposed here is to experimentally study in full detail emergence in the quantum world, all the way from the microscopic physics of elementary (atomic) constituents to a hierarchy of effective models at large scales. A central objective will be to verify emerging models, probe the limits of their validity, when do they break down, and investigate how big a system has to be to show emergent phenomena. Ultra-cold atoms allow to implement and study complex, interacting quantum many body systems in detail and powerful manipulation techniques combined with the ability to measure each atom with close to unit efficiency offers an unprecedented way to probe the whole path of emergence from micro- to macro physics We will investigate three examples: (i) Emergence of quantum field theories as illustrated by the sine-Gordon model; (ii) emergence of universality as the system forgets its initial conditions in the course of non-equilibrium evolution; (iii) emergence of a hydrodynamic description in the non-equilibrium evolution of correlated quantum systems. We envision robust, verified emergent models to have numerous applications as quantum simulators ranging from solid state physics to aspects of physical system that are inaccessible for direct experiments. Moreover, emergence coming from inaccessibility of knowledge about the microscopic world may ultimately lead to a natural bridge between quantum and classical.