Entropy, information, and order are important concepts in many fields, relevant for materials to machines, for biology to econophysics. Entropy is typically associated with disorder; yet, the counterintuitive notion that a thermodynamic system of hard particles (colloids) might - due solely to entropy - spontaneously assemble from a fluid phase into an ordered crystal was first predicted in the mid-20th century. First demonstrated for rods, and then spheres, the ordering of colloids by entropy maximization upon crowding is now well established. In recent years, surprising discoveries of ordered entropic colloidal crystals of extraordinary structural complexity have been predicted by computer simulation and observed in the laboratory. These findings, presented in this talk, demonstrate that entropy alone can produce order and complexity beyond that previously imagined, and that, in situations where other interactions are also present, the role of entropy in producing order may be greatly underestimated. Glotzer discusses how new statistical mechanical principles learned from recent findings can be used to design shapes that promote long-range entropic order.