A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. Two fundamental challenges to any such approach are, at the conceptual level, the role of time in the emergent context and, technically, the fact that the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics and quantum field theory to the problem. We initiate a study of such problems using spin systems as toy models for emergent geometry and gravity. These are models of quantum networks with no a priori geometric notions. In this talk we present two models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This is essentially a Hubbard model on a dynamical lattice. We will see that regions of high connectivity behave like analogue black holes. Particles in their vicinity behave as if they are in a Schwarzchild geometry. Time permitting, I will show our study of the entanglement entropy of the system, which suggests particle localization near these traps.