Carbon sequestration is increasingly being promoted as a potential response to the risks of unrestrained emissions of CO2, either in place of or as a complement to reductions in the use of fossil fuels. However, the potential role of carbon sequestration as an (at-least partial) substitute for reductions in fossil fuel use can be properly evaluated only in the context of a long-term acceptable limit (or range of limits) to the increase in atmospheric CO2 concentration, taking into account the response of the entire carbon cycle to artificial sequestration. Under highly stringent emission-reduction scenarios for non-CO2 greenhouse gases, 450 ppmv CO2 is the equivalent, in terms of radiative forcing of climate,to a doubling of the pre-industrial concentration of CO2. It is argued in this paper that compliance with the United Nations Framework Convention on Climate Change (henceforth, the UNFCCC) implies that atmospheric CO2 concentration should be limited, or quickly returned to, a concentration somewhere below 450 ppmv. A quasi-one-dimensional coupled climate-carbon cycle model is used to assess the response of the carbon cycle to idealized carbon sequestration scenarios. The impact on atmospheric CO2 concentration of sequestering a given amount of CO2 that would otherwise be emitted to the atmosphere, either in deep geological formations or in the deep ocean, rapidly decreases over time. This occurs as a result of a reduction in the rate of absorption of atmospheric CO2 by the natural carbon sinks (the terrestrial biosphere and oceans) in response to the slower buildup of atmospheric CO2 resulting from carbon sequestration. For 100 years of continuous carbon sequestration, the sequestration fraction (defined as the reduction in atmospheric CO2 divided by the cumulative sequestration) decreases to 14% 1000 years after the beginning of sequestration in geological formations with no leakage, and to 6% 1000 years after the beginning of sequestration in the deep oceans. The difference (8% of cumulative sequestration) is due to an eflux from the ocean to the atmosphere of some of the carbon injected into the deep ocean.The coupled climate-carbon cycle model is also used to assess the amount of sequestration needed to limit or return the atmospheric CO2 concentration to 350–400 ppmv after phasing out all use of fossil fuels by no later than 2100. Under such circumstances, sequestration of 1–2 Gt C/yr by the latter part of this century could limit the peak CO2 concentration to 420–460 ppmv, depending on how rapidly use of fossilfuels is terminated and the strength of positive climate-carbon cycle feedbacks. To draw down the atmospheric CO2 concentration requires creating negative emissions through sequestration of CO2 released as a byproduct of the production of gaseous fuels from biomass primary energy. Even if fossil fuel emissions fall to zero by 2100, it will be difficult to create a large enough negative emission using biomass energy to return atmospheric CO2 to 350 ppmv within 100 years of its peak. However, building up soil carbon could help in returning CO2 to 350 ppmv within 100 years of its peak. In any case, a 100-year period of climate corresponding to the equivalent of a doubled-CO2 concentration would occur before temperatures decreased. Nevertheless, returning the atmospheric CO2concentration to 350 ppmv would reduce longterm sea level rise due to thermal expansion and might be sufficient to prevent the irreversible total melting of the Greenland ice sheet, collapse of the West Antarctic ice sheet, and abrupt changes in ocean circulation that might otherwise occur given a prolonged doubled-CO2 climate. Recovery of coral reef ecosystems, if not already driven to extinction, could begin.