The coelacanth has long been regarded as a "living fossil," with extant specimens looking very similar to fossils dating back to the Cretaceous period. The hypothesis of a slowly or even not evolving genome has been proposed to account for this apparent morphological stasis. While this assumption seems to be sustained by different evolutionary analyses on protein-coding genes, recent studies on transposable elements have provided more conflicting results. Indeed, the coelacanth genome contains many transposable elements and has been shaped by several major bursts of transposition during evolution. In addition, comparison of orthologous genomic regions from the genomes of the 2 extant coelacanth species L. chalumnae and L. menadoensis revealed multiple species-specific insertions, indicating transposable element recent activity and contribution to post-speciation genome divergence. These observations, which do not support the genome stasis hypothesis, challenge either the impact of transposable elements on organismal evolution or the status of the coelacanth as a "living fossil." Closer inspection of fossil and molecular data indicate that, even if coelacanths might evolve more slowly than some other lineages due to demographic and/or ecological factors, this variation is still in the range of a "non-fossil" vertebrate species.