In hard materials, geometric frustration (GF) is most often associated with the disruption of long-range order in the bulk and proliferation of defects in the ground state. Soft and self-assembled materials, on the other hand, are composed of intrinsically flexible building blocks held together deformable and non-covalent forces. As such, soft assemblies systems are able to tolerate some measure of local misfit due to frustration, allowing imperfect order to extend over at least some
finite range.

This talk will overview an emerging paradigm for self-organized soft materials, geometrically-frustrated assemblies (GFAs), where interactions between self-assembling elements (e.g. particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting
protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells and phase-separated lipid vesicles. In assemblies, GF leads to a host of anomalous structural and thermodynamic
properties, including heterogeneous and internally-stressed equilibrium structures, self-limiting assembly and topological defects in the equilibrium assembly structures.

I will highlight the some of the basic principles and common outcomes of GF in soft matter assemblies, as well as, outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems. Finally, I will describe opportunities and challenges to exploit the scale-dependent thermodynamics of GFA to engineer new classes of intentionally ill-fitting assemblies that target equilibrium architectures with well-defined dimensions on length scales that extend far beyond the size of the building blocks or their interactions.