Frustrated assemblies are comprised of ill-fitting building blocks whose favored local relative arrangement cannot be globally realized. In fact, most self assembled structures contain some degree of frustration. In some cases, the frustration is locally resolved and leads to little or no structural consequence, while in other cases it dominates the assembly's size, shape, and response properties.

In this talk, I will present different manifestations of geometric frustration as they naturally arise in molecular crystals, liquid crystals, spin systems, and nanoparticle assemblies. To theoretically study these assemblies we resort to an intrinsic approach in which matter is described only through local properties available to an observer residing within the material. The frustration is then quantified by the geometric compatibility conditions whose structure allows us to classify the frustration and predict the assembly's behavior without explicitly solving for the ground state of the system.