  We review Fermi's paradox (or the "Great Silence" problem), not only arguably
the oldest and crucial problem for the Search for ExtraTerrestrial Intelligence
(SETI), but also a conundrum of profound scientific, philosophical and cultural
importance. By a simple analysis of observation selection effects, the correct
resolution of Fermi's paradox is certain to tell us something about the future
of humanity. Already a more than three quarters of a century old puzzle - and a
quarter of century since the last major review paper in the field by G. David
Brin - Fermi's paradox has generated many ingenious discussions and hypotheses.
We analyze the often tacit methodological assumptions built into various
answers to this puzzle and attempt a new classification of the numerous
solutions proposed in an already huge literature on the subject. Finally, we
consider the ramifications of various classes of hypotheses for the practical
SETI projects. Somewhat paradoxically, it seems that the class of
(neo)catastrophic hypotheses gives, on balance, the strongest justification for
guarded optimism regarding our current and near-future SETI efforts.
