Nitrogen fixation is one of the important biochemical pathways that play a role in controlling the oceanic nitrogen inventory. Here we review nitrogen fixation in the ocean, with a particular emphasis on Trichodesmium, one of the dominant marine diazotrophs. Distribution data for diazotrophs are scarce, except in specific regions where Trichodesmium is known to bloom. Although some regions are clearly under-sampled, Trichodesmium can generally be found in tropical regions where temperature is at least 20 °C, except in the North Atlantic, where drift to higher latitudes is possible via the Gulf Stream. Likewise, biomass estimates are problematic because of the colony-forming habit of this organism. Trichodesmium grows slowly with reported maximum growth rates of approximately 0.14 d-1. Studies of the photosynthetic physiology indicate that Trichodesmium can tolerate high light intensity with Ik and Ic values of ∼300 and ∼140 μmole photons m−2 s−1, respectively. Review of the elemental composition of Trichodesmium indicates that the C:N molar ratio of 6.3:1 does not depart significantly from the predicted Redfield stoichiometry of 6.6:1. Overall, measured N:P ratios from the field and the laboratory were around 50, a significant departure from the Redfield stoichiometry of 16:1. Whether this indicates phosphorus limitation is not clear at present. The iron requirements of diazotrophs in general and of Trichodesmium in particular have been the subject of debate, but some recent laboratory studies have converged on Fe:C (μmole:mole) of approximately 50 at 70% of the maximum growth rates (μmax) to 250 at μmax for this species. There is a noticeable lack of information on growth rate as a function of phosphorus and fixed nitrogen sources. Although Trichodesmium is a non-heterocystous cyanobacterium, carbon and nitrogen fixation co-occur during the light period, indicating that light energy is required for both of these processes. This is likely to be achieved through cellular differentiation of the trichomes and a tight control of the temporal expression of many biochemical pathways. A summary table presents a set of values for the initial parameterisation of parameters relevant to the incorporation of nitrogen fixation in biological and biogeochemical models.