The eleven year solar activity cycle is a remarkable example of regular behavior emerging from an extremely turbulent system. The jets on Jupiter sit unmoving on a sea of turbulent eddies. Astrophysical phenomena often display organization on spatial and temporal scales much larger than the turbulent processes that drive them. An outstanding problem of astrophysics (and indeed other branches of nonlinear physics) is how to describe the statistics of systematic behavior emerging from the underlying chaos, given that Direct Numerical Simulation of these objects is simply impossible. Here, I shall introduce these fascinating phenomena and describe how methods from non-equilibrium statistical mechanics and many body quantum systems may be developed to give some insight into their behavior.