Methane (CH4) emissions from Arctic polygonal tundra are spatially heterogeneous due to the complex soil hydrology. This spatial heterogeneity in CH4 emissions requires a reliable upscaling approach to reach accurate regional CH4 budgets in the Arctic tundra. Additionally, Arctic regions have been warming two to four times faster than the global average in recent decades. CH4 emission from the Arctic is increasing under climate warming. However, interactions among temperature, soil water table and vegetation complicate a full understanding of emission rates and their magnitude in a changing climate. In this dissertation, I applied the CLM-Microbe model to examine microtopographic impacts on CH4 and CO2 fluxes across seven landscape types in Utqiaġvik, Alaska: trough, low-centered polygon (LCP) center, LCP transition, LCP rim, high-centered polygon (HCP) center, HCP transition, and HCP rim. Low-elevation and thus wetter landscape types (i.e., trough, transitions, and LCP center) had larger CH4 emissions rates with greater seasonal variations than high-elevation and drier landscape types (rims and HCP center). Substrate availability for methanogenesis was identified as the most important factor determining CH4 emission. Upscaled CH4 emissions at the eddy covariance (EC) domain using an area-weighted approach were underestimated by 20% and 25% at daily and hourly time steps. Combined with three footprint algorithms, I upscaled CH4 fluxes from a plot level to EC domains (200 m × 200 m) for three sites in Utqiaġvik (US-Beo, US-Bes, and US-Brw), one in Atqasuk (US-Atq) and one in Ivotuk (US-Ivo). Three footprint algorithms are the homogenous footprint (HF) that assumes even contribution of all grid cells, the gradient footprint (GF) that assumes gradually declining contribution from center grid cells to edges, and the dynamic footprint (DF) that considers the impacts of wind and heterogeneity of land surface. DF performed better than HF and GF algorithms in capturing the temporal variation in daily CH4 flux in each month, while the model accuracy was similar among the three algorithms due to flat landscapes. Temporal variations in CH4 flux during 2013-2015 were predominately explained by air temperature (67-74%), followed by precipitation (22-36%). Spatial heterogeneities in vegetation and elevation dominated spatial variations in CH4 flux for all EC domains despite relatively weak differences in simulated CH4 flux among three footprint algorithms. Finally, I projected CH4 emissions during 2016-2100 for all these five sites under three Shared Socioeconomic Pathways (SSP) scenarios derived from three climate models. CH4 emission exhibited a stronger response (630 - 850% increase) under SSP5-8.5 than under SPP1-2.6 and SSP2-4.5, likely supported by a simultaneous enhanced precipitation-induced expansion of anoxic conditions for methanogenesis. All three CH4 transport pathways (i.e. diffusion, ebullition, and plant-mediated transport) are increasing by 2100, and ebullition contributed most to CH4 emissions under three SSP scenarios across five sites. Temperature sensitivity for CH4 emission differed using three climate models (i.e., BCC-CSM2-MR, CESM2, and EC-Earth3) with a Q10 range of 2.7-60.9 under SSP1-2.6, 3.8-17.6 under SSP2-4.5, and 5.7-17.2 under SSP5-8.5. This study advanced our understanding of the mechanisms of current and future CH4 emissions in the highly heterogeneous Arctic landscape. The CLM-Microbe model was testified as a powerful tool that can simulate CH4 flux at both plot and landscape scales at a high temporal resolution, upscale terrestrial CH4 flux integrated with an appropriate algorithm, and project future CH4 emissions in Arctic landscapes under different climate scenarios.