The main purpose of this talk is to describe, by way of concrete examples, how the field of numerical relativity now contributes to our understanding of open questions in gravitational collapse, heavy-ion physics, and turbulence. I will begin by motivating these studies in terms of the physical systems they are intended to clarify,then provide specific examples of how to describe these systems with numerical simulations of asymptotically AdS spacetimes in the fully non-linear regime of general relativity.