AbstractBackground and aims – At one time it was believed that without reasonable fossil evidence the phylogeny of any group of organisms was almost unknowable. And so fossils were sought, found and their significance duly proclaimed. Such a dominating viewpoint slowly disappeared in the 1970s and 1980s and data derived from the structure of extant organisms were given more attention. At the same time, molecular data became accessible as another source of phylogenetic information and, eventually, it was believed – as it was with fossils before – that without reasonable molecular evidence the phylogeny of any group of organisms is almost unknowable. Justification for this view has been sought in the explanation that, in general, morphology is misleading (convergence, parallelisms, etc.). These same views have come to prevail in diatom phylogenetic studies. A problem with this constellation of viewpoints is that if morphology is so misleading then so too are fossils (which are, after all, morphological specimens). This paper addresses some of these issues. Methods – Discussion and analysis of classification, past and present, and discussion and analysis of the role played by characters (homologies), taxa and fossils in the search for a comprehensive classification. Conclusion – Classification is equivalent to phylogeny. Sources of data (evidence) are morphology, palaeontology and molecules. Morphology and palaeontology, when understood as derived from specimens (character-bearers), are the same thing. No data source has any unique privilege over another. Stories explaining away character conflict have no place in scientific studies.