  This perspective will overview an emerging paradigm for self-organized soft
materials, {\it geometrically-frustrated assemblies}, 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, geometric frustration 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. The
purpose of this perspective is to 1) highlight the unifying principles and
consequences of geometric frustration in soft matter assemblies, 2) to classify
the known distinct "modes" of frustration and review corresponding experimental
examples, and 3) to describe outstanding questions not yet addressed about the
unique properties and behaviors of this broad class of systems.
