Reverse-engineering and understanding the regulatory dynamics of genes is key to gaining insights into many biological processes on molecular level. Advances in genomics technologies and decreasing costs of DNA sequencing enabled interrogating relevant properties of the genome, collectively referred to as epigenetics, on very large scale. This work presents results from two collaborative projects with experimental biologists and two new general computational methods for analysis of high-throughput epigenomic data. The first collaborative project is joint work with Dr. Kathrin Plath and members of her lab at UCLA on studying the epigenetics of somatic cell reprogramming in mouse. By generating and analyzing a large compendium of genomics datasets at four distinct stages during reprogramming, we discovered key properties of the regulatory dynamics during this process and proposed new ways to improve its efficiency. The first computational method in this work, ChromTime, presents a novel framework for modeling spatio-temporal dynamics of chromatin marks. ChromTime detects expanding, contracting and steady domains of chromatin marks from time course epigenomics data. Applications of the method to a diverse set of biological systems show that predicted dynamic domains likely mark important regulatory regions as they associate with changes in gene expression and transcription factor binding. Furthermore, ChromTime enables analyses of the directionality of spatio-temporal dynamics of epigenetic domains, which is a previously understudied aspect of chromatin dynamics. Our results uncover associations between the direction of expanding and contracting domains of several chromatin marks and the direction of transcription of nearby genes. The second collaborative project is joint work with cancer researchers, Dr. Lynda Chin and Dr. Kunal Rai and members of their labs at MD Anderson Cancer Center in Houston, TX. Within this project we studied the epigenetics of melanoma cancer progression. Our collaborators generated genome-wide maps for a large number of histone modifications, DNA methylation and gene expression in tumorigenic and non-tumorigenic human melanocytes. By comparing these maps we discovered that loss of acetylation marks at regulatory regions is characteristic of tumorigenic melanocytes and that modulating acetylation levels can impact tumorigenic potential of cells. In addition, we developed a novel nanostring assay for interrogating the chromatin state at a small subset of genomic locations, which can potentially be used for diagnostic or prognostic purposes in future. The second computational method presented in this work, CSDELTA, is designed to detect differential chromatin sites from genome-wide chromatin state maps in groups with multiple samples. Biological relevance of detected differential sites is supported by associations with changes in gene expression and transcription factor binding. Furthermore, CSDELTA models the functional similarity between chromatin states and improves upon the resolution of detection compared to existing methods, which enables more accurate downstream analyses to gain insights into the regulatory dynamics of biological systems.