The ocean can be considered as a chemical reactor, whose energy sources are the various matter inputs originating from the continent and the ocean. Among various elements, carbon plays a key role as it is involved in both inorganic form as CO{2} and organic forms such as compounds synthesized through photosynthesis. Thus, the ocean is presently an active actor in climate change and ocean-atmosphere exchange processes. This review will present some insights into: 1) schematic representations of the carbon cycle, with emphasis on CO{2} exchange between the ocean and the atmosphere and to the organic parts of this cycle, 2) concepts relative to the biological pump of CO{2}, with a detailed view on photosynthesis, 3) concepts leading to the existence of oceanic provinces and associated productivity for open sea and coastal areas, 4) addressing the question: what is the net efficiency of the biological pump of CO{2 }in terms of exportation of organic carbon and sequestration in sediments and 5) specific aspects on biogeochemical processes occurring at the boundary between the ocean and the atmosphere.