The three-dimensional organization of the genome plays a major role in modulating biological processes such as gene expression and DNA replication, which are crucial to establishment and maintenance of cell identity in human development. Recent technological advances have enabled the creation of high-resolution maps of chromatin architecture genome-wide from which to test new biological hypotheses. In this thesis, we first present a networks based algorithm, 3DNetMod, for identifying the prominent feature of Topological Associating Domains (TADs) and their inner subTADs in high resolution Chromosome-Conformation-Capture Hi-C data. We then apply our method to chromatin dynamics during mitosis, uncovering how TADs and subTADs evolve temporally. Afterwards, we classify TADs/subTADs by the presence of other genome folding features, compartments and loops, as well as cohesin and CTCF placement and correlate with replication initiation enrichment. We show that perturbing looping TAD boundaries both locally and globally affects initiation placement, thus, genome folding architecture plays a functional role in replication. Finally, as part of the 4D-Nucleome consortium analysis, we integrate genome folding with other features of nuclear spatial positioning (SPIN states) and transcription. We show a common unifying trend amongst these multimodal features. This work results in a better understanding of the dynamical aspects of chromatin folding and how it influences and coincides with other various biological mechanisms, including aspects of DNA replication timing.