About the Osteolepidae
It is believed that the Osteolepiformes gradually evolved into the first amphibians. Osteolepids have certain features that are also found in the oldest known amphibians. One of the most important is that the bones of their pectoral and pelvic fins were the precursors of terrestrial limbs. A few evolutionary stages further and these fins would evolve into legs used to travel on land. These then became amphibians (tetrapods), which in turn became reptiles, mammals, and eventually us. Fishes like Osteolepis can therefore be regarded as our ancestors.
Another important indication that osteolepids are ancestral to tetrapods is that they most probably possesed an air bladder which also could be used as a respiratory organ. Osteolepids are regarded as a sister-group of the Dipnoi (lungfishes)