The epithelial-mesenchymal transition (EMT) plays an important role in cancer metastasis and drug resistance, and involves epigenetic remodeling. However, how epigenetic changes affect the dynamical traits such as plasticity or memory is not fully understood. In this thesis, we analyze the effects of epigenetic feedback on EMT through integrating the effects of this feedback on various aspects of the miR-200/ZEB loop – a core circuit regulating EMT. Epigenetic feedback on the inhibition of miR-200 by ZEB can largely stabilize the mesenchymal state, thus making the process irreversible. Follow-up preliminary experiments show that when EMT is induced in epithelial cells, a certain percentage of cells can stay in the mesenchymal state even after the inducing signal is removed. This percentage depends on the extent of induction of EMT, thus well recapitulating our model-based predictions. Beyond the irreversibility of EMT, we also investigate the irreversibility of MET, or equivalently, resistance to EMT. We identify the epigenetic regulation acting on the ZEB1/GRHL2 link as a key determinant of driving an irreversible MET. Furthermore, we focus on the E/M hybrid state, and show that it can be stabilized as compared to the fully mesenchymal phenotype if NRF2 can influence SNAIL at an epigenetic level, as this link makes transitions out of hybrid state more difficult. Finally, we explore a general feature of the observed multi-stability, the lack of correlation between landscape and corresponding transition rates.