Geometrically frustrated assembly, where locally preferred motifs are incompatible with constraints on global ordering of the assembly, may result in a super-extensive energy penalty to assembly growth and self-limitation of the assembly size. Using theory and simulation, we study how this mechanism may also shape the assembly's boundary and its interior packing, which are distinct morphological changes. In Chapter 1, we provide some background and a theoretical framework for understanding self-limiting behavior due to geometric frustration. Three distinct projects are detailed in the subsequent chapters: original numerical results are presented on competing responses to frustration in helical bundles made of chiral filaments in Chapter 2, a novel tilt-curvature coupling and its consequences in microphase separated chiral rod membranes are illustrated by both numerical and theoretical results in Chapter 3, and a new particle model for simulation of saddle-wedge membrane assemblies with new theoretical advancement of a continuum model and new numerical results are presented in Chapter 4. In Chapter 5, we conclude by considering lessons from this work for future engineering of self-limiting materials.