Dangerous climate change is best avoided by drastically and rapidly reducing greenhouse gas emissions. Nevertheless, geoengineering options are receiving attention on the basis that additional approaches may also be necessary. Here we review the state of knowledge on large-scale ocean fertilization by adding iron or other nutrients, either from external sources or via enhanced ocean mixing. On the basis of small-scale field experiments carried out to date and associated modelling, the maximum benefits of ocean fertilization as a negative emissions technique are likely to be modest in relation to anthropogenic climate forcing. Furthermore, it would be extremely challenging to quantify with acceptable accuracy the carbon removed from circulation on a long term basis, and to adequately monitor unintended impacts over large space and time-scales. These and other technical issues are particularly problematic for the region with greatest theoretical potential for the application of ocean fertilization, the Southern Ocean. Arrangements for the international governance of further field-based research on ocean fertilization are currently being developed, primarily under the London Convention/London Protocol.