Although uranium concentration in seawater is only about 3 micrograms per liter, the quantity of uranium dissolved in the world's oceans is estimated to amount to 4.5 billion tonnes of uranium metal (tU). In contrast, the current conventional terrestrial resource is estimated to amount to about 17 million tU. However, for a number of reasons the extraction of significant amounts of uranium from seawater remains today more a dream than a reality. Firstly, pumping the seawater to extract this uranium would need more energy than what could be produced with the recuperated uranium. Then if trying to use existing industrial flow rates, as for example on a nuclear power plant, it appears that the annual possible quantity remains very low. In fact huge quantities of water must be treated. To produce the annual world uranium consumption (around 65,000 tU), it would need at least to extract all uranium of 2 x 10$^{13}$ tonnes of seawater, the volume equivalent of the entire North Sea. In fact only the great ocean currents are providing without pumping these huge quantities, and the idea is to try to extract even very partially this uranium. For example Japan, which used before the Fukushima accident about 8,000 tU by year, sees about 5.2 million tU passing every year, in the ocean current Kuro Shio in which it lies. A lot of research works have been published on the studies of adsorbents immersed in these currents. Then, after submersion, these adsorbents are chemically treated to recuperate the uranium. Final quantities remain very low in comparison of the complex and costly operations to be done in sea. One kilogram of adsorbent, after one month of submersion, yields about 2 g of uranium and the adsorbent can only be used six times due to decreasing efficiency. The industrial extrapolation exercise made for the extraction of 1,200 tU/year give with these values a very costly installation installed on more than 1000 km$^2$ of sea with a lot of boats for transportation and maintenance. The ecological management of this huge installation would present significant challenges. This research will continue to try to increase the efficiency of these adsorbents, but it is clear that it would be very risky today, to have a long-term industrial strategy based on significant production of uranium from seawater with an affordable cost.