  For more than four decades, scientists have been trying to find an answer to
one of the most fundamental questions in paleoclimatology, the `faint young Sun
problem'. For the early Earth, models of stellar evolution predict a solar
energy input to the climate system which is about 25% lower than today. This
would result in a completely frozen world over the first two billion years in
the history of our planet, if all other parameters controlling Earth's climate
had been the same. Yet there is ample evidence for the presence of liquid
surface water and even life in the Archean (3.8 to 2.5 billion years before
present), so some effect (or effects) must have been compensating for the faint
young Sun. A wide range of possible solutions have been suggested and explored
during the last four decades, with most studies focusing on higher
concentrations of atmospheric greenhouse gases like carbon dioxide, methane or
ammonia. All of these solutions present considerable difficulties, however, so
the faint young Sun problem cannot be regarded as solved. Here I review
research on the subject, including the latest suggestions for solutions of the
faint young Sun problem and recent geochemical constraints on the composition
of Earth's early atmosphere. Furthermore, I will outline the most promising
directions for future research. In particular I would argue that both improved
geochemical constraints on the state of the Archean climate system and
numerical experiments with state-of-the-art climate models are required to
finally assess what kept the oceans on the Archean Earth from freezing over
completely.
