The global physical potential of different methods of carbon dioxide removal (CDR) from the atmosphere is reviewed. A new categorisation into plant-based, algal-based and alkalinity-based approaches to CDR is proposed. Within these categories, the key flux-limiting resources for CDR are identified and the potential CO2 removal flux that each technology could generate is quantitatively assessed – with a focus on the present, 2050 and 2100. This reveals, for example, that use of waste nutrient flows to feed macro-algae for biomass energy with carbon capture and storage (algal BECCS), shows significant CDR potential, without needing the large land areas or freshwater supplies of plant biomass energy crops. Adding up the potentials of different CDR methods, the total CDR potential at present is 1.5–3 PgC yr−1 (Petagram of carbon per year), comparable in size to either the natural land or ocean carbon sinks. Already 0.55–0.76 PgC yr−1 of this potential has been realised through afforestation and inadvertent ocean fertilisation. The total CDR potential (without including direct air capture) grows such that by mid-century it is 4–9 PgC yr−1 and by the end of the century it is 9–26 PgC yr−1, comparable with current total CO2 emissions of 10 PgC yr−1. The CDR that can be realised under social, economic and engineering constraints is always going to be less than the physical potential. Nevertheless, if combined with reducing CO2 emissions (conventional mitigation), CDR has the physical potential to help stabilise atmospheric CO2 by the middle of this century.