The Carboniferous was an important time in the evolution of the vertebrates. The transitional "fish-amphibians" with their many fingered feet were replaced by terrestrial amphibians in the first radiation of the tetrapods. The Early Carboniferous salamander-like Balanerpeton shown here was the first member of the amphibian group known as the temnospondyls. The Late Carboniferous Ptyonius shown below belonged the lepospondyl group of amphibians.
Amongst the fishes, palaeoniscids and acanthodians were still important, but the distinctive Devonian cephalaspids, pteraspids and placoderms were gone. Sharks and coelacanths were important in both marine and fresh waters. The earliest known lampreys occur in the Early Carboniferous of Bear Gulch and the Late Carboniferous of Mazon Creek.
With reference to Dawkins' book "The Ancestor's Tale" we have illustrations of concestors 17 (Balanerpeton), (18 would be represented by one of the Devonian lungfish), 19 (Caridosuctor), 20 (for example one of the palaeoniscids), 21 (Harpagofutator)) and 22 (Mayomyzon).