It is important that climate models can accurately simulate the terrestrial carbon cycle in the Arctic due to the large and potentially labile carbon stocks found in permafrost-affected environments, which can lead to a positive climate feedback, along with the possibility of future carbon sinks from northward expansion of vegetation under climate warming. Here we evaluate the simulation of tundra carbon stocks and fluxes in three land surface schemes that each form part of major Earth system models (JSBACH, Germany; JULES, UK; ORCHIDEE, France). We use a site-level approach in which comprehensive, high-frequency datasets allow us to disentangle the importance of different processes. The models have improved physical permafrost processes and there is a reasonable correspondence between the simulated and measured physical variables, including soil temperature, soil moisture and snow. We show that if the models simulate the correct leaf area index (LAI), the standard C3 photosynthesis schemes produce the correct order of magnitude of carbon fluxes. Therefore, simulating the correct LAI is one of the first priorities. LAI depends quite strongly on climatic variables alone, as we see by the fact that the dynamic vegetation model can simulate most of the differences in LAI between sites, based almost entirely on climate inputs. However, we also identify an influence from nutrient limitation as the LAI becomes too large at some of the more nutrient-limited sites. We conclude that including moss as well as vascular plants is of primary importance to the carbon budget, as moss contributes a large fraction to the seasonal CO2 flux in nutrient-limited conditions. Moss photosynthetic activity can be strongly influenced by the moisture content of moss, and the carbon uptake can be significantly different from vascular plants with a similar LAI. The soil carbon stocks depend strongly on the rate of input of carbon from the vegetation to the soil, and our analysis suggests that an improved simulation of photosynthesis would also lead to an improved simulation of soil carbon stocks. However, the stocks are also influenced by soil carbon burial (e.g. through cryoturbation) and the rate of heterotrophic respiration, which depends on the soil physical state. More detailed below-ground measurements are needed to fully evaluate biological and physical soil processes. Furthermore, even if these processes are well modelled, the soil carbon profiles cannot resemble peat layers as peat accumulation processes are not represented in the models. Thus, we identify three priority areas for model development: (1) dynamic vegetation including (a) climate and (b) nutrient limitation effects; (2) adding moss as a plant functional type; and an (3) improved vertical profile of soil carbon including peat processes.