The very early universe is expected to have involved explosive and non-perturbative phenomena when a scalar field condensate decays into large, non-thermal fluctuations of itself and other bosonic fields coupled to it. A major example is the process of preheating after inflation, when the inflaton decays and leads eventually to the thermal bath of the Hot Big Bang. These phenomena generate a stochastic background of gravitational waves, which carries unique information about their dynamics and the underlying high-energy physics. In this talk, I will first review the analytical and numerical methods that we have developed to compute the gravity wave spectrum produced by such cosmological sources. I will then discuss two different cases in detail: preheating after hybrid inflation and the non-perturbative decay of super-symmetric flat directions. In each case, I will pay special attention to the relevance of the resulting gravity waves for upcoming interferometric experiments like Advanced LIGO. If time permits, I will also present a work in progress on the effects of vector fields on the gravity waves produced by such out-of-equilibrium sources.