There are a few species of fish that don’t have scales or fins. One example is the hagfish, which is a primitive, eellike creature that scavenges dead and dying fish. Hagfish are scaleless and finless, but they do have external gills and a simple brain. Another example is the Lamprey, a parasitic fish that latches onto other fish and sucks their blood. Lampreys also don’t have scales or fins, but they do have sucker-like mouths lined with sharp teeth.