Conodonts were small, thin, elongate jawless creatures that were a common component of the marine fauna from the late Cambrian, throughout the Palaeozoic and into the Triassic. For the majority of conodont research history, speculations on conodont affinity were restricted to the histology and arrangement of their mineralized tissues—‘conodont elements’. These conodont elements comprise millimetre‐scale phosphatic microfossils that superficially resemble teeth, and are commonly recovered from the residues of appropriately aged, disaggregated sedimentary rocks. It has only been in the last three decades, since the discovery of exceptionally preserved soft tissues, that the debate on conodont affinity has been refined, though it has hardly been less vigorously debated. Despite being studied extensively for over more than a century and a half, conodonts retain significant enigmatic qualities. Although many geologists today are familiar with the name, knowledge of conodont biology and ecology are often surprisingly lacking or confused, and conodonts remain as largely disembodied microfossil curiosities. Despite this, conodont elements are extensively and variously used in biostratigraphy, thermal maturation studies and palaeoenvironmental reconstructions, while conodonts themselves occupy a potentially critical position in the evolutionary tree of our own phylum—the chordates.