We evaluate suggestions to harness the ability of calcifying organisms (molluscs, crustacea, corals and coccolithophore algae) to remove permanently CO2 from the atmosphere into solid (crystalline) CaCO3 for atmosphere remediation. Here, we compare this blue carbon with artificial/industrial Carbon dioxide Capture & Storage (CCS) solutions. An industrial CCS facility delivers, at some cost, captured CO2, nothing more. But aquaculture enterprises cultivating shell to capture and store atmospheric CO2 also produce nutritious food and perform many ecosystem services like water filtration, biodeposition, denitrification, reef building, enhanced biodiversity, shoreline stabilisation and wave management. We estimate that a mussel farm sequesters three times as much carbon as terrestrial ecosystems retain. Blue carbon farming does not need irrigation or fertiliser, nor conflict with the use of scarce agricultural land. Blue carbon farming can be combined with restoration and conservation of overfished fisheries and usually involves so little intervention that there is no inevitable conflict with other activities. We calculate that this paradigm shift (from ‘shellfish as food’ to ‘shellfish for carbon sequestration’) makes bivalve mollusc farming and microalgal farming enterprises, viable, profitable, and sustainable, alternatives to all CCUS industrial technologies and terrestrial biotechnologies in use today.