Living fossil

Living fossil is an informal term for any living species of organism which appears to be the same as a species otherwise only known from fossils and which has no close living relatives. These species have all survived major extinction events, and generally retain low taxonomic diversities. A species which successfully radiates (forming many new species after a possible genetic bottleneck) has become too successful to be considered a "living fossil". However, the term is frequently misinterpreted.

Overview
There is a subtle difference between a "living fossil" and a "Lazarus taxon". A Lazarus taxon is a taxon (either one species or a group of species) that suddenly reappears, either in the fossil record or in nature (i.e. as if the fossil had "come to life again"), while a living fossil is a species that (seemingly) hasn't changed during its very long lifetime (i.e. as if the fossil has always lived). The mean species turnover time (the time a species lasts before it is replaced) varies widely among the phyla, but averages about 2-3 million years. So, a living species that was thought to be extinct (e.g. the coelacanth, Latimeria chalumnae) is not a living fossil simply due to that definition (though it may still be one because it hasn't changed much), it is a Lazarus species. Coelacanths disappeared from the fossil record some 80 million years ago (upper Cretaceous). If, however, other Cenozoic Latimeria fossil species were to be found, the coelacanth would be considered a true living fossil, as that would fill in the gap where the species is "dead". Of course, species do not just appear out of thin air, so all living Lazarus species (excluding disappearing and reappearing red list species) are nonetheless considered living fossils, if it can be shown they are not Elvis taxa.

Some living fossils are species that were known from fossils before living representatives were discovered. The most famous examples of this are the coelacanthiform fishes Latimeria chalumnae and Latimeria menadoensis and the dawn redwood, Metasequoia, discovered in a remote Chinese valley. Others include glypheoid lobsters, mymarommatid wasps, and jurodid beetles, all of which were first described from fossils, but later found alive (2 species, 10 species, and one species respectively). Others are a single living species with no close living relatives, but which is the survivor of a large and widespread group in the fossil record, perhaps the best-known example of which is Ginkgo biloba (the ginkgo), though there are others, such as the Syntexis libocedrii (the cedar wood wasp).

Note that just because a living fossil is a surviving representative of an archaic lineage does not necessarily require that it retains all of the "primitive" features (plesiomorphies) of the lineage it is descended from; that is, they may possess one to many derived features (autapomorphies), that have evolved since the time of their lineage's divergence. All that is required is that they can be unambiguously assigned to an otherwise extinct lineage (rarely are they identical to the fossil forms). See for example the uniquely and highly autapomorphic oxpeckers, which are not "true" living fossils (as no fossils are known yet) but nonetheless appear to be the only survivors of an ancient lineage related to starlings and mockingbirds.

Note the similarity between the 170 million year old fossil Ginkgo sp. leaves on the left, and the living plant on the right.