Trilobites are an iconic group of extinct arthropods that lived in Palaeozoic oceans for c. 270 Ma, before their demise at the end of the Permian Period. Despite their considerable diversity (> 22 000 species) and abundance, particularly in Cambrian and Ordovician rocks, as well as intensive study for well over 200 years, trilobite systematics remains in a state of flux. In this contribution, the complex history of trilobite classification over the last century is briefly reviewed, including the seminal scheme published by Henry Swinnerton in 1915. The cryptogenesis problem, which relates to the supposedly obscure phylogenetic links between major post-Cambrian trilobite clades and their Cambrian sister taxa, is also discussed. Previous studies have suggested that the cryptogenesis problem is largely a taxonomic artefact, but the Cambrian origins of some post-Cambrian groups, such as the orders Proetida and Odontopleurida, are still unclear. Future directions for research on trilobite systematics are outlined, from taxonomic studies involving comprehensive documentation and extensive illustration of morphology at the species level, through to broad-scale phylogenetic analyses that initiate or test hypotheses about relationships across the major groups. Other ongoing issues to be addressed include identifying the sister group of Trilobita, and determining whether certain taxa, such as the suborder Agnostina and Cambrian family Burlingiidae, represent trilobites.