Authigenic seafloor carbonate crusts include fenestrate microbialite, thrombolite, and four types here designated Fine-grained Crust, Sparry Crust, Hybrid Sparry Fine-grained Crust, and Sparry Crust plus Coarse Grains. Each of the latter four types includes at least some layered examples that have generally been regarded as stromatolites. Recognition and interpretation of these various deposits assists understanding of stromatolite development. Sparry Crust is common in the Late Archaean-Mesoproterozoic. It includes botryoidal fans and other crystal pseudomorphs, microdigitate stromatolite, dendrite, isopachous laminite, and herringbone calcite. Although differing in primary mineralogy and bedform, these are all characterized by coarse sparry, commonly radial fibrous, fabric and appear light coloured in thin-section. They have commonly been referred to as seafloor cement, although they formed at the open sediment-water interface rather than as void-fills. Two of them in particular, isopachous laminite and microdigitate ‘tufa’, typically form isopachous layers with good vertical inheritance and have been regarded as stromatolites. In contrast to Sparry Crust, Fine-grained Crust has fine-grained (micritic, clotted, peloidal, filamentous) microfabric that appears dark in thin-section, and irregular uneven layering with relatively poor inheritance. Mixed crusts, composed of millimetric alternations of Sparry and Fine-grained crust, are here termed Hybrid Sparry Fine-grained Crust. Sparry Crust with coarse allochthonous grains - here termed Sparry Crust plus Coarse Grains – includes some examples that have been given formal stromatolite names, e.g., Gongylina and Omachtenia. Sparry, Hybrid, and Fine-grained crusts are common components of Precambrian stromatolites. Their relative abundances change through time. Archaean stromatolite fabrics are commonly obscured by recrystallization, but their preserved lamina arrangements suggest that many of them could be composed mainly of Sparry or Hybrid crust. During the Palaeoproterozoic-Mesoproterozoic, Sparry Crust fabrics were common in peritidal stromatolites, whereas Hybrid Crust appears to have dominated large subtidal domes and columns. Fine-grained Crust may not have become generally abundant until the Neoproterozoic, when it commonly formed both stromatolites and thrombolites. Phanerozoic normal marine stromatolites are also typically composed of Fine-grained Crust. Present-day analogues of Sparry Crust fabrics occur in some speleothem, hot spring, and splash-zone marine crusts, and of Fine-grained Crust in lithified microbial mats. Light-dark millimetric alternations of sparry and fine-grained crust that characterize Hybrid Crust have analogues in freshwater stromatolites. Taken together, these comparisons suggest that some Precambrian stromatolites are abiogenic, some microbial, and others are intimate hybrid mixtures of the two, and that - preservation permitting - these varieties can be distinguished using microfabric and lamina criteria.