Tightly packed ordered arrays of atoms exhibit remarkable collective optical properties, as dissipation in the form of photon emission is correlated. In this talk, I will discuss the many-body out-of-equilibrium physics of atomic arrays, and their potential to realize versatile light-matter interfaces. I will focus on the problem of Dicke superradiance, where a collection of excited atoms synchronizes as they decay, emitting a short and intense pulse of light. Superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. I will show that superradiance is a universal phenomenon in ordered arrays, and generically occurs if the inter-atomic distance is small enough. Our predictions can be tested in state of the art experiments with arrays of neutral atoms, molecules, and solid-state emitters and pave the way towards understanding the role of many-body decay in quantum simulation, metrology, and lasing.