Lapworth’s paper on ‘The Moffat Series’ (1878) provided a model for deciphering the ‘interminable greywackes’ of the Southern Uplands, and one which lasted for a century. The same paper established graptolites in a dominant position in Lower Palaeozoic biostratigraphy. The changes in the biostratigraphic paradigm are discussed with reference to Lapworth’s contribution; issues implicit in his 1878 paper are still contentious. Graptolites have exemplified the conflict that can arise between the use of fossils as stratigraphic ciphers, on the one hand, or as complex organisms to be interpreted biologically on the other. They have been subjected to the vicissitudes of stratigraphic fashion. It is shown that Lapworth’s biostratigraphy has been enduring in contrast to his structural or palaeogeographic interpretations. However, the subsequent separation of litho- and chrono- from biostratigraphy, while conceptually necessary, has encouraged an idealistic pursuit of the perfect stratigraphic section for the purpose of defining stratigraphic boundaries. This has not always been constructive, not least because such boundaries often coincide with events which militate against the preservation of ideal sections. But Lapworth’s close integration of biostratigraphic range with observations on lithology, ‘barren beds’ and fossil preservation may have a new lease of life in the context of event stratigraphy.