Ultracold atoms in optical lattices form a unique testbed for quantum many-body physics. Using such systems it has recently become possible to engineer strongly-correlated materials from the ground up and probe them with single-atom resolution. I will describe experiments in which we have synthesized the first magnetic material composed of ultracold atoms, and watched it undergo a quantum phase transition from a paramagnet to an antiferromagnet. I will then introduce a new algorithmic cooling scheme that we have employed to drive strongly correlated gases to yet-lower temperatures, and discuss ways to apply these techniques to fundamental questions in topological materials, many-body dynamics and beyond.