Conodonts are an enigmatic group of eel-like animals whose only mineralised parts are toothlike microfossils located in the oral cavity of the animal. Conodonts are common fossils in marine rocks from the late Cambrian to the late Triassic. Despite their abundance and their importance for solving biostratigraphic and geologic problems, their phylogenetic affinity has been the centre of a hot debate for over a century. They have been regarded as a primitive vertebrates or chordates, possibly providing the earliest evidence of skeletonization within vertebrate phylogeny. In collaboration with Phil Donoghue (University of Bristol) our research is focused on their functional morphology and evolutionary relationships based on the applications of state of the art tomographic and computational analysis.