  Stellar evolution models predict that the solar luminosity was lower in the
past, typically 20-25 % lower during the Archean (3.8-2.5 Ga). Despite the
fainter Sun, there is strong evidence for the presence of liquid water on
Earth's surface at that time. This "faint young Sun problem" is a fundamental
question in paleoclimatology, with important implications for the habitability
of the early Earth, early Mars and exoplanets. Many solutions have been
proposed based on the effects of greenhouse gases, atmospheric pressure,
clouds, land distribution and Earth's rotation rate. Here we review the faint
young Sun problem for Earth, highlighting the latest geological and geochemical
constraints on the early Earth's atmosphere, and recent results from 3D global
climate models and carbon cycle models. Based on these works, we argue that the
faint young Sun problem for Earth has essentially been solved. Unfrozen Archean
oceans were likely maintained by higher concentrations of CO2, consistent with
the latest geological proxies, potentially helped by additional warming
processes. This reinforces the expected key role of the carbon cycle for
maintaining the habitability of terrestrial planets. Additional constraints on
the Archean atmosphere and 3D fully coupled atmosphere-ocean models are
required to validate this conclusion.
