The greater part of a monkfish is made up of the head, which is normally discarded, although the part of meat just below the eye, called the cheek, can be eaten. In general, however, the only part of the monkfish sold commercially is the tail. Because the rib cage is discarded with the head, there are no pin-bones to worry about. There is just the large spinal column that runs through the tail, and this can be easily removed by cutting down each side.