Abstract To avoid global warming in excess of 1.5°C under the current sluggish adoption of drastic reductions in global greenhouse gas emissions, application of methods to remove carbon dioxide from the atmosphere will become essential in the near future; yet, development of these methods is in its infancy. Land-based methods are further developed than marine methods, but it is likely that similar-scaled application will be necessary in both realms. There are many misconceptions in discussion groups and fora about the ‘simplicity’ or ‘ease’ of proposed marine applications, partly because the complex marine carbon cycle is insufficiently understood by the proponents, having been discussed in largely inaccessible, technical texts only. This review outlines the basic operation of the marine carbon cycle in straightforward terms, with some simplifications, to help advance the debate among the wider community. Break-out boxes provide additional detail where desired, and references (and the sources cited therein) provide avenues for further study. The review then discusses two potential marine methods for atmospheric carbon removal that are thought to offer the greatest potential in terms of carbon removal mass: ocean iron fertilization and ocean alkalinity enhancement. Finally, six statements/arguments that seem to regularly crop up in carbon removal discussion groups are evaluated within the perspective of the compiled and reviewed information.