The wonder of evolution is that although no organism is a complete living fossil, all are to some extent living fossils.
A living fossil is a life forms that is found today and resembles a life form seen in a fossil specimen. The living fossil concept in a way suggests that a species can persist unchanged over a geological span of time. But how persistent can it be and, then, where does it come from? Certainly, this concept should not be understood as a proposal or evidence for ad-hoc creation without derivation from a precursor form. Similarity does not mean identity. Evolution can happen without striking changes at the macroscale. Yet, differences may become apparent by detailed, microscopic inspection and comparative study.A. J. Werth and W. A. Shear, 2014.
The term living fossil was coined by Charles Darwin. Werth and Shear write that Darwin—like modern biologists— was struck by the resemblance of lungfish anatomy, comparing the large lungs, cartilaginous notochord and fleshy, lobed fins of the current species of Protopterus, Neoceratodus and Lepidosiren of Africa, Australia and South America, respectively, with morphological forms of lungfishes found in the fossil record.
Realizing that there is no unifying definition for living fossils, Werth and Shear point out that the term living fossil is a problematic oxymoron. But despite its ambiguity this living phrase still has valuable lessons to teach in evolution, ecology and taxonomy.
Alexander J. Werth and William A. Shear: The Evolutionary Truth About Living Fossils. American Scientist November-December 2014, 102 (6), pp. 434-443.