Epistasis refers to the phenomenon that phenotypic consequences caused by mutation of one gene depend on one or more mutations at another gene. Epistasis is critical for understanding many genetic and evolutionary processes, including pathway organization, evolution of sexual reproduction, mutational load, ploidy, genomic complexity, speciation and the origin of life. However, the epistatic dynamics in biological systems under various internal and external perturbations are largely unknown. In this study, I firstly focused on exploring dynamics of epistasis between duplicate genes. I then investigated the properties of global epistatic networks under different traits. Finally I examined the dynamic changes of epistatic relations among genes under genetic and environmental perturbations. I started my research by investigating the transcriptional dynamics of duplicate genes with negative epistasis under external perturbations. We found an interesting design principle that two epistatically interacting duplicate genes can acquire a fitness advantage under fluctuating environmental perturbations by achieving maximum expression levels asynchronously. Soon after finishing this project, instead of focusing on epistatic relations between duplicate genes, we analyzed a high-throughput experimental dataset investigating epistatic interactions among ~4,000 genes in baker's yeast, Saccharomyces cerevisiae. We showed that epistasis is prevalent (~13% increase from the random expectations) and displays modular architecture among genes that underlie the same growth traits. More interestingly, our results indicate that hub genes responsible for the same growth traits tend to link epistatically with each other more frequently than random expectation. When conducting these projects, we realized that few studies have examined the genome-wide dynamics of epistatic relations under different genetic and environmental perturbations, which might be due to limitations in screening epistatic relations for multiple mutants of the same genes or multiple environmental conditions under the current high-throughput experimental platforms. We addressed this issue theoretically by using Flux Balance Analysis (FBA), which involves the optimization of cellular objective functions and allows prediction of in silico flux values and/or growth. A series of unique properties of epistatic dynamics under various genetic and environmental perturbations have been revealed in our FBA simulations, and some of them are highly consistent with previous experimental studies.