Abstract: Chemical bonds are among the most fundamental concepts in science. They describe the way in which atoms associate to form molecules and compounds, and they have been a central paradigm of science for a century. Today, powerful software packages that solve quantum mechanical theories of chemical bonding are in routine use to predict molecular and crystal structures. Are analogous capabilities possible for predicting colloidal crystals, where nanoparticles play the role of atoms?  In this talk, we discuss a remarkable finding that has emerged from twenty years of global nanoscience research: Aside from differences in length, time and energy scales, atoms and nanoparticles can self-assemble into identical crystal structures, including those with large, complex unit cells. These colloidal crystal structures are possible even in the absence of explicit nanoparticle interactions, further demonstrating that statistical thermodynamics is agnostic to the forces driving self-assembly. What sort of “bonding” describes these structures, which emerge as the particles become crowded and are stabilized solely by entropy maximization? We discuss these questions and present a new theory of entropic bonding that has intriguing analogies with chemical bonding theory. With entropic bonding theory, we can predict colloidal crystal structures from nanoparticle shape in the same way that chemical bonding theory predicts atomic crystal structures from electronic valence.