The Sarcopterygii, or lobe-fin fishes comprise one of two living lineages of bony fishes, the Osteichthyes. The other lineage is the Actinopterygii - the ray-finned fishes.
Although ray-finned fishes are the largest and most successful vertebrae lineage, one lobe-fin group was very successful and gave rise to the four-legged vertebrates - the tetrapods (including humans). One group (clade) of lobefin fishes, the Lungfishes (Dipnoi) has a fossil history dating back to the early Devnian, more thanr 400 million years ago. Lungfishes are the closest living sister taxon to the tetrapods.
Lobe-fins have fleshy pectoral and pelvic fine that are each joined to the body by a single bone. The pectoral fins articulate with the shoulder via the humerus (the same bone we have in our upper arm) and the pelvic fins articulate to the pelvis via the femur (our upper leg bone).
The lobe-fins first appeared in the fossil record during the Lower Devonian period, and became very successful. Today, however, there are only eight living lobe-fins: two species of coelocanth and six species of lungfish.
Clement AM, Ahlberg PE (2014) The First Virtual Cranial Endocast of a Lungfish (Sarcopterygii: Dipnoi). PLoS ONE 9(11): e113898. doi:10.1371/journal.pone.0113898