Disorder is the rule, rather than the exception, in nature. Despite this, we understand little about how disorder affects interacting quantum matter. I will give an overview of our experiments using ultracold atom gases to probe paradigms of interacting disordered quantum particles. We introduce disorder to naturally clean atomic gases cooled to billionths of a degree above absolute zero using focused optical speckle. I will explain how we observe Anderson localization—a spectacular phenomenon in which interference prevents waves from propagating in a disordered medium—of quantum matter in three dimensions. I will also show how we combine speckle with an optical crystal to emulate a completely tunable and precisely characterized disordered quantum solid. In these optical lattice experiments, we realize disordered Hubbard models that we use to answer critical questions regarding how disorder impacts the properties of electronic solids, such as superconductors and metals.