The extensive literature on the capacity to offset fossil fuel carbon emissions by enhancing terrestrial carbon sinks or biomass energy substitution is confused by different interpretations of the word 'potential'. This paper presents an overview of these capacities for the world, the EU 15 countries and the UK over the next 50-100 years, divided into what are considered: (i) theoretical potential capacities, (ii) realistic potential capacities, and (iii) conservatively achievable capacities. The range of capacities is determined principally by judgements of the areas of land that are likely to be devoted to sequestration or energy crops. Theoretically, enhanced carbon sequestration and energy cropping could offset 2000-5000 Mt C/yr globally, but a more realistic potential offset is 1000-2000 Mt C/yr and there are good reasons to suppose that only 200-1000 Mt C/yr is actually achievable. Similarly, 'conservative achievable' estimates for the EU15 and the UK are about 10 times less than theoretical potentials. In the EU15, 'realistic potential' and 'conservative achievable' estimates for energy crop substitution were 21-32% and 11-21% of current annual emissions, respectively, compared with 5-11% and 2-5% for carbon sequestration. In the UK, the 'realistic potential' and 'conservative achievable' estimates for energy crop substitution were 3.4-13.6% and 0.7-4.1% of current annual emissions, respectively, compared with 2.0-3.4% and 0.7-1.3% for carbon sequestration.