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. We use these optical lattice experiments to probe the impact of interactions in the Hubbard model on localization. I will discuss evidence for many-body localization observed in transport experiments in an optical lattice.