The Adelaide Geosyncline is a deeply subsident Neoproterozoic to Middle Cambrian basin complex in South Australia with a record of at least five major successive rift cycles. Each rift system has its own locus and orientation. Although the rift events led to the breakup of the Neoproterozoic supercontinent Rodinia, of which, according to the SWEAT hypothesis, Australia was a part juxtaposed against western Laurentia, the timing of breakup has been controversial. The author favours the interpretation that continental separation commenced soon after the last major Neoproterozoic rift phase associated with the Sturtian glaciation at ~700 Ma. The stratigraphic record of the Adelaide Geosyncline has been divided into twelve sequence-sets (S-S), each comprising two or more sequences, and separated by breaks in sedimentation. Mafic volcanism and intrusion of northwest-trending dykes at ~827 Ma marked the first onset of rifting after a brief period of deposition in a stable intracratonic basin (S-S Willouran 1). The second phase of rifting (S-S Willouran 2) produced narrow, deeply subsident northwest-trending grabens filled with mixed evaporitic clastic and carbonate sediments, and minor associated mafic volcanism. The third rift phase (S-S Torrensian 1) initiated faulting along the north-south Torrens Hinge Zone and widened the zone of crustal extension; there was minor mafic and local felsic (~777 Ma) volcanism. Terrestrial to shallow marine clastics and minor carbonates overlapped the Willouran grabens onto basement of the Willouran rift shoulders. S-S Torrensian 2 and 3 were deposited in the later stages of this rift phase, with clastic wedges derived from adjacent cratons shedding into the rift basin and interfingering with more distal fine-grained clastic and carbonate sediments. Sedimentation of S-S Torrensian 2 occurred at a time of generally low relative sea level, accompanied by deposition of dolomite and sedimentary magnesite in marginal marine and lagoonal environments, and coarse sandy facies in proximal zones. S-S Torrensian 3 records the first major marine inundation of the basin. S-S Sturtian 1 represents renewed basement uplift followed by marine transgression, but this S-S is only partially preserved due to regional erosion at the base of the Sturtian glacials. S-S Sturtian 2 contains all the Sturtian glacigenic sediments, and was accompanied by the fourth major rift episode. Crustal extension at this time produced mainly northwest-trending grabens peripheral to the Curnamona Province, and essentially defined the limits of this basement block. S-S Sturtian 3 is marked by the first major marine transgression onto the Gawler Craton, and represents a sag phase of sedimentation believed to be associated with the initiation of continental separation. S-S Marinoan 1 continues to record sag-phase deposition but with a prevailing lower sea level at first, followed by a rise. Marinoan glaciation is represented by S-S Marinoan 2, with possibly three sequences recording the waxing, maximum and waning stages of the glaciation, but the Adelaide Geosyncline is likely to have lain just north of the palaeoequator and south of the main continental ice sheet. S-S Marinoan 3 and 4 are two major post-glacial transgressive-regressive cycles. Local growth faulting in South Australia, and mafic volcanism in western New South Wales, during the latest Neoproterozoic may represent rifting associated with accelerated separation, but it is not yet certain that the NSW volcanics were extruded on the same continental margin as the Adelaide Geosyncline. Similarly, the position of northwestern Tasmania, with its Neoproterozoic basement, remains uncertain despite the presence of probable Marinoan glacials on King Island. Three sequence sets have previously been recognised in the Early to Middle Cambrian, with deposition in the Arrowie (in the north) and Stansbury (in the south) Basins. In the later Early Cambrian, a renewed phase of crustal extension produced the east to northeast-trending Kanmantoo Trough, which was filled with extremely thick clastic sediments immediately prior to compressive and transpressive deformation in the Delamerian Orogeny in the latest Early to Late Cambrian, associated with syntectonic I- to marginally S-type granitic magmatism, followed by post-tectonic A-type intrusions. Delamerian plate convergence may have involved collision of a Neoproterozoic micro-continent and/or Cambrian volcanic arcs with the Neoproterozoic Australian southeastern continental margin.