During the last decade or so, tremendous system modeling efforts have been made to quantify the role of Arctic ecosystems in the global climate system. However, ecosystem and biogeochemical feedbacks resulting from complex hydrological and thermal dynamics related to permafrost aggradation-degradation are inadequately represented in current Earth System Models (ESMs). Existing studies with these ESMs unequivocally showed that there is a large uncertainty in the feedbacks - some studies suggested that the greenhouse gas emissions from large carbon reservoirs in permafrost and soils would exert a significant positive feedback while other studies indicated that the positive feedback is small using biogeochemistry models coupled with permafrost dynamics models of various complexities. Here we report a number of key limitations of the current ESMs in representing permafrost dynamics and associated uncertainty sources for the feedback by presenting our research progress on quantifying permafrost thawing and its effects on emissions of CO2 and CH4 from terrestrial and aquatic ecosystems in the Arctic. Our progress ranges from process-based modeling of permafrost and hydrological dynamics, to their impacts on greenhouse gas emissions, and to their feedbacks to the global climate system. In the end, we will recommend ways to improve the current ESMs through further developing a suite of models of permafrost and hydrological dynamics, vegetation dynamics, carbon and methane dynamics. With the enhanced ESMs, we intend to test the hypothesis - There exists a warming feedback that enhances permafrost degradation to stimulate CO2 and CH4 emissions from a large reservoir of soil and permafrost carbon, which in turn, intensifies warming at the global scale. The magnitude of the positive feedback is determined by the complex interaction among changes in Arctic's landscape, hydrology, vegetation and permafrost degradation and aggradation at various spatial and temporal scales.