The Tasman Line, a much-discussed concept in the geology and tectonics of eastern Australia, has a long and chequered history of interpretation. This extends to current debates regarding the age and position of the Tasman Line in Gondwana–Rodinia reconstructions. We present constraints, from mapping, geochemistry and geophysics, on the interpretation of gravity and magnetic lineaments attributed to the Tasman Line in New South Wales, South Australia, Victoria and Tasmania. These pieces of evidence suggest a protracted and complex latest Neoproterozoic to Carboniferous geological history that produces a variety of geophysical responses, rather than a simple ‘Line’. We also find no evidence of Rodinian breakup age activity responsible for any of the anomalies. In light of these findings, our preference is that the Tasman Line concept be abandoned as misleading, especially with regard to models of Rodinia–Gondwana breakup, which must have occurred elsewhere, possibly well to the east. Instead, the rocks preserved in the westernmost part of the Tasmanides are consistent with previously proposed ‘Southwest Pacific’-style models for Neoproterozoic continental breakup, margin formation and reaccretion of continental fragments in the Early Palaeozoic.