Leatherback sea turtles are part of an order known as the testudines. This order includes all turtles, tortoises and terrapins.   It is believed that turtles evolved from a land dwelling species called  Eunotosaurus  roughly 260 million years ago.  The  Eunotosaurus  had ribs but no shell and teeth. The next discovery dates back 220 million years ago to the first marine inhabitant known as the Odontochelys semitestacea. The discovery of this creature showed how the ribs were a  vestigial structure and widened to begin forming the top shell through evolution which came into picture roughly 10 million years later with Proganochelys quenstedti.  The shell of a turtle is also an analogous structure. 

In the phylogeny above, you can see where the  different families diversify or have gone extinct permanently.  The leatherback sea turtle is the last known species in the dermochelyidae family.  They differ from other species based on their color, size and rubbery leather like skin.