Large standing crops of phytoplankton are often found in the neighbourhood of shelf-sea fronts. How do these large biomasses come about? Special hypotheses have been proposed, but it seems preferable to treat frontal production in terms of a general theory. By assuming that phytoplankton behave as `passive contaminants of water motion' and that vertical turbulent mixing is the dominant factor, it is possible to model the distribution of phytoplankton at fronts by means of simple expressions for photosynthesis, nutrient-controlled growth, and grazing. Because of their strong vertical and horizontal gradients, fronts are good places to test such simple models, which might also be applied to primary production in other regions of the ocean.