To understand the Neotethyan ophiolites better, their place in the history of the host basins is explored, using the Jurassic Hellenic–Dinaric and some Cretaceous (mainly peri-Arabian) ophiolites as examples. These formed in mature (c. 60 Ma and 100 Ma old) seaways by spreading at rates that apparently were too high to persist for more than a fraction of the basin history. Each ophiolite group formed in a short time interval, about 10 Ma, soon after changes in the motions of plates in the host basins. Therefore, these ophiolites do not seem to have formed by normal long-term spreading along mid-ocean ridges, but their formation signifies special ‘ophiolite events’. This fits well the widely accepted origin in a supra-subduction zone (SSZ) setting that was inferred from geochemical data. The ophiolites studied here are thus interpreted as having formed in new subduction zones that originated during changes in plate motions. The spreading during their accretion was driven by fast retreat (roll-back) of the subducting slabs. The western ophiolites of the Hellenic–Dinaric belt, dominated by mid-ocean ridge basalt (MORB)-like rocks but invaded by SSZ magmas, could have formed along ridges just before they failed (collapsed), but the age data fit better formation in a proto-back-arc setting alongside the more eastern ophiolites with the typical SSZ signature. The construction of the ophiolites examined here ended when they were detached from their substrate and pushed over the adjacent basins. At that stage they were underplated by metamorphic soles, but how the latter were emplaced still needs clarification. Continuing retreat of the subducting slabs consumed the host basins and pushed the ophiolites hundreds of kilometres until they were obducted over the nearby margins 15–20 Ma after formation. This framework seems to apply to many ophiolites and allows us to interpret them in terms of known processes, but also highlights problematic issues that still need to be resolved.