“More is different”, P. W. Anderson famously wrote in the 1970’s. Understanding how complex phenomena emerge from the simple macroscopic rules of many-body systems has a long history and is an ongoing challenge today. Modern experimental techniques such as ultra-cold atomic systems make it possible to create near-perfect realizations of many-body theories. In particular, strongly interacting cold gases of atoms in excited states with high principle quantum number (Rydberg atoms) can be used to study phenomena ranging from kinetic constraints reminiscent of glassy systems to non-equilibrium phase transitions characterizing the spreading of diseases or the onset of turbulence. Here we review our recent experimental and theoretical studies of such a system, which can be regarded as a semiclassical many-body simulator.