A series of recent studies on extant coelacanths has emphasised the slow rate of molecular and morphological evolution in these species. These studies were based on the assumption that a coelacanth is a 'living fossil' that has shown little morphological change since the Devonian, and they proposed a causal link between low molecular evolutionary rate and morphological stasis. Here, we have examined the available molecular and morphological data and show that: (i) low intra-specific molecular diversity does not imply low mutation rate, (ii) studies not showing low substitution rates in coelacanth are often neglected, (iii) the morphological stability of coelacanths is not supported by paleontological evidence. We recall that intra-species levels of molecular diversity, inter-species genome divergence rates and morphological divergence rates are under different constraints and they are not necessarily correlated. Finally, we emphasise that concepts such as 'living fossil', 'basal lineage', or 'primitive extant species' do not make sense from a tree-thinking perspective.