The invention relates to a device for trimming the surface of meat, in particular fish fillets, comprising a transporting element by means of which the products which are to be processed are conveyed continuously in the transporting direction T into the region of a knife head, also comprising an element for detecting the position of the products, as well as a knife head for trimming the products and a means of controlling the movement of the knife head in dependence on the information and data determined by the position-detecting element, the device being distinguished in that the knife head is designed for automatically executing free trimming cuts along the surface contour of the products. The invention also relates to an apparatus for processing meat using a device mentioned above, and to a corresponding surface-trimming method.