Living fossil is an informal term for any living species (or clade) 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".
Example: Ginkgo, Whisk ferns (Psilotum), cockroach, coelacanth fish etc.