Entropy is typically associated with disorder; yet, the counterintuitive notion that particles with no interactions other than excluded volume might self-assemble from a fluid phase into an ordered crystal has been known since the mid-20th century. First predicted for rods, and then spheres, the thermodynamic ordering of hard shapes by nothing more than crowding is now well established. In recent years, surprising discoveries of entropically ordered colloidal crystals of extraordinary structural complexity have been predicted by computer simulation and observed in the laboratory. Colloidal quasicrystals, clathrate structures, and structures with large and complex unit cells typically associated with metal alloys, can all self-assemble from disordered phases of identical particles due solely to entropy maximization. In this talk, we show how entropy alone can produce order and complexity beyond that previously imagined, both in colloidal crystal structure as well as in the kinetic pathways connecting fluid and crystal phases. We show examples of fluid-fluid transitions that precede crystallization, just as in certain molecular liquids and protein solutions, but arising solely from entropy. To better understand these phenomena, we introduce the (loose) notion of the entropic bond and show how we can engineer shape for entropy maximization. We show how tools use by the quantum community to predict atomic crystal structures can be used to predict entropic colloidal crystals.