Class Sarcopterygii
Tree of Life
  

Class Sarcopterygii
(The Lobe Finned Fishes)

Phylum Chordata
Subphylum Vertebrata
Infraphylum Gnathostomata
Superclass Osteichthyes
Class Sarcopterygii

Also See:
Class Sarcopterygii Fish Fossils
Sarcopterygii (from Greek meaning flesh fin) contains the so called lobe-finned fishes, further divided into the coelacanths and lungfish. Importantly, the limb like fins of sarcopterygiians are so similar to the expected ancestral form of tetrapod limbs that the scientific consensus has emerged they are the ancestors all tetrapods. Sarcopterygians are placed in the Osteichthyes group (bony fishes), because their skeleton is bone rather than cartilage, and are therefore most closely related to the Actinopterygians. The oldest which appear in the late Silurian closely resemble the Acanthodians. 
    Class Sarcopterygii
      Actinistia
        Eoactinistia
        Subclass Coelacanthimorpha
          Order Coelacanthiformes
            Family Latimeriidae
              Macropoma
              Latimeria
      Rhipidistia (ancestors of the tetrapods)
         Subclass Dipnoi
           Order Ceratodontiformes
           Order Lepidosireniformes
         Subclass Tetrapodomorpha
           Order Rhizodontida
          Superorder Osteolepidida
            Order Osteolepiformes
              Family Osteolepidae
              Family Tristichopteridae
                Eusthenopteron
                Hyneria
              Order Panderichthyida
                Tiktaalik
                Tetrapoda

The Sarcopterygians lineage split in the lower Devonian into the Coelacanths and the Rhipidistia. The fossil records suggests that the Coelacanths peaked during the Carboniferous. They were believed to have gone extinct at the end of the Cretaceous, until the genus Osteolepis lobe finned fishLatimeria was discovered off the east coast of South Africa in 1938; since then, other Latimeria have been discovered in Kenya, Mozambique, Tanzania, Madagascar, and South Africa. Coelacanths are often considered to be living fossils.

Rhipidistians appeared with the Coelacanths, but migrated from marine to freshwater habitats, probably initially near the mouths of rivers. The Rhipidistia lineage split into two major groups, lungfishes and tetrapodomorphs. The lungfishes evolved the earliest primitive lungs and limbs, peaked in the Triassic, and remain an extant though minor taxon. Lungfishes used their stubby fins to walk on land and find new water if their waterhole was depleted, with their lungs breathing air, just like modern species do. Rhipidistia is now understood to be an ancestor for the whole of Superclass Tetrapoda. The tetrapodomorphs had essentially the same anatomy as lungfishes. Tetrapods comprise amphibians, reptiles, dinosaurs, birds, and mammals and even snakes by descent, the groups that would go on to dominate the land, and result in the appearance humans very, very recently.

 Also see: Museum Fish Fossils