Abstract Precambrian and younger basins reflect the interaction of sediment supply and subsidence; the latter is generally ascribed to tectonic, magmatic and related thermal processes. The interplay of supply and subsidence is further modified by eustasy and palaeoclimate. Problems and enigmas inherent in analysis of Precambrian basin-fills include: a spectrum of ideas on the maximum age of Phanerozoic-style plate tectonics in the rock record; Archaean heat flow up to two to three times present values; changes in magmatism over time (including global magmatic events); the evolution of atmospheric composition and of life and their influence on weathering, erosion and sediment supply rates; degree of preservation, deformation and metamorphism, and preservational bias (especially of intracratonic basins which would lack evidence for early plate tectonics); a limited rock record; poor age constraints, inherent errors in geochronological techniques and difficulty in dating the time of deposition of sedimentary rocks. Major influences on Precambrian basin formation are assumed to include magmatism, plate tectonics, eustasy and palaeoclimate, all of which interacted. Models for greenstone belt evolution include plate tectonic intra-oceanic generation, plume-generated oceanic plateau, and global catastrophic magmatic events that may have been transitional to a plate tectonic regime over several hundred million years. The latter transition may have included the onset of the supercontinent cycle. Insignificant preservation of Precambrian ocean floor makes evaluation of these models problematic. Eustasy was intrinsically related to continental crustal growth rates, continental freeboard and the hypsometric curves of emerging cratons. Possible maximum crustal growth rates near the Archaean–Proterozoic boundary led to globally elevated sea levels, and the formation of enormous carbonate-banded iron formation platforms where cyanobacterial mats, which produced oxygen, flourished. The combination of changes in cratonic growth rates, thermal elevation of cratons, eustasy, weathering and palaeo-atmosphere composition may have combined to produce the first global glaciation at ca. 2.4–2.2 Ga. Examples of basins discussed here emphasise the interaction of tectonism, magmatism, eustasy and palaeoclimate in their evolution. For the Neoarchaean Witwatersrand basin (Kaapvaal craton, South Africa), evidence for all these factors is preserved in the basin-fill, whereas for the Neoproterozoic Macaubas basin (Sao Francisco craton, Brazil), clear evidence for eustasy is more limited. The ca. The origin of greenstone basins remains contentious. That magmatism was a major factor in their evolution is accepted by most, but whether this was plate-independent or plate-driven is less certain; the role of mantle plumes and the possibility of greenstones having been ridge-generated are also discussed by some workers. Episodic magmatism on a global scale may have played a role in the evolution of early basins such as the greenstones, Witwatersrand and Ventersdorp, and with a possible transition to plate tectonics into the Palaeoproterozoic, mid-ocean ridge growth related to either supercontinent break-up or to continental crustal growth rates probably influenced the eustatically controlled Hamersley and Lower Transvaal basin sedimentation. The possibility that early plate tectonics was characterised by variable spreading and subduction rates is discussed in the light of evidence from the Witwatersrand basin, the North American, Baltic and Siberian cratons, and the Transvaal Supergroup. In conclusion, Precambrian basin evolution probably reflects the variable interaction of tectonism, magmatism, eustasy and palaeoclimate (as also found for Phanerozoic basins), with the most significant difference compared to younger basins lying in the relative rates of processes such as ridge-spreading, subduction, crustal growth, weathering and atmospheric compositional change.