This paper reviews the current status of using remote sensing and process-based modeling approaches to assess the contemporary and future circumpolar carbon balance of Arctic tundra, including the exchange of both carbon dioxide and methane with the atmosphere. Analyses based on remote sensing approaches that use a 20-year data record of satellite data indicate that tundra is greening in the Arctic, suggesting an increase in photosynthetic activity and net primary production. Modeling studies generally simulate a small net carbon sink for the distribution of Arctic tundra, a result that is within the uncertainty range of field-based estimates of net carbon exchange. Applications of process-based approaches for scenarios of future climate change generally indicate net carbon sequestration in Arctic tundra as enhanced vegetation production exceeds simulated increases in decomposition. However, methane emissions are likely to increase dramatically, in response to rising soil temperatures, over the next century. Key uncertainties in the response of Arctic ecosystems to climate change include uncertainties in future fire regimes and uncertainties relating to changes in the soil environment. These include the response of soil decomposition and respiration to warming and deepening of the soil active layer, uncertainties in precipitation and potential soil drying, and distribution of wetlands. While there are numerous uncertainties in the projections of process-based models, they generally indicate that Arctic tundra will be a small sink for carbon over the next century and that methane emissions will increase considerably, which implies that exchange of greenhouse gases between the atmosphere and Arctic tundra ecosystems is likely to contribute to climate warming.