In this talk I will describe our ongoing effort at the University of Chicago to explore exotic models of condensed matter using materials made of light. Starting with a quick discussion of "light as matter," I will then explain how we imbue photons with the essential attributes of a material particle: mass, charge, and interactions. Along the way, I will introduce the two "flavors" of photons that we employ for our photonic matter: optical photons trapped in Fabry-Perot cavities, and microwave photons trapped in superconducting resonators or transmon qubits. Finally, I will describe the first two materials that have emerged from our interacting photons: a Mott insulator of microwave photons and a topological fluid of optical photons. More broadly, building materials from light impacts both (a) the kinds of matter that can be assembled, and (b) the assembly process itself, providing a new window on the physics of correlated quantum matter.