Shi studied fractionalization in frustrated quantum matter, where the interacting spins are unable to order. Instead, they create long-range patterns of entanglement leading to states of matter such as quantum spin liquids, heralding the topological quantum matter with novel fractionalized particles and emergent gauge fields. These states are characterized by topological order: ground state degeneracy on a manifold of non-zero genus, and fractionalized excitations with abelian and non-abelian quantum statistics. In these states, the original localized spin degrees undergo further fractionalization to give new degrees of freedom, such as Majorana fermions and spinons. In these states, both charges and spins are localized. However, the emergent fractionalized degrees of freedom can be remarkably delocalized and able to transport energy. Identifying and studying the phenomena of fractionalization presents a dual challenge: discerning fractionalized particles and finding material candidates that realize fractionalization. His dissertation presents a comprehensive theoretical study of fractionalization in both one and two dimensions, focusing on these challenges. [Link to his dissertation]