The main purpose of this talk is to describe, in detail, how the field of numerical relativity now contributes to our understanding of open questions in heavy-ion physics, turbulence, and the thermalization of quantum systems. This is made possible with the advent of the AdS/CFT duality, which conjectures that certain quantum systems at strong coupling admit a description in terms of classical gravity. I will begin by motivating our effort in terms of the physical systems that it is meant to clarify. I will then provide concrete examples of the holographic approach of describing these physical systems with gravity toy models, using our own group's simulations of asymptotically AdS spacetimes in the fully non-linear regime of general relativity.