The three-dimensional organization of the genome plays a critical role in the regulation of gene expression and the establishment and maintenance of cell identity in human development. Recent technological advances have enabled the creation of high-resolution maps of chromatin architecture both at specific regions of interest and across entire mammalian genomes, creating significant demand for computational tools to keep pace with the creation of new datasets testing diverse biological hypotheses. In this thesis, we use Chromosome-Conformation-Capture sequencing data to elucidate how chromatin contacts are rewired during cell state transitions. We first present computational and statistical methods to identify unique topological patterns across length scales in high-resolution Chromosome-Conformation-Capture-Carbon-Copy (5C) and Hi-C data. These methods include approaches for both (1) identifying cell type-specific looping interactions and contact domain boundaries and (2) integrating 3D genome topology with epigenetic modifications across the linear epigenome. We then apply our methods to test biological hypotheses in model systems of somatic cell reprogramming, architectural protein depletion, and chromatin dynamics during mitosis. The application of our tools to these datasets sheds light on the relationships between cellular state, biophysical processes, and genetic and epigenetic information on the linear DNA polymer. Taken together, this thesis presents a collection of computational and statistical tools designed to reduce the bias and noise in genome folding datasets and to identify and quantify cellular state-specific genome folding features such as long-range looping interactions, TADs, and stripes. By applying these tools to disease-relevant model systems, we contribute to a novel 3D topological understanding of the etiology of human disease and significantly advance our knowledge of how information encoded in the one-dimensional genome catalyzes the higher-order folding patterns in the three-dimensional nucleus.