Rare but extreme events are known to have dramatic influence on the statistics of turbulent flows, but are notoriously hard to handle both analytically and numerically. As alternative approach methods borrowed from field theory, most notably the instanton approach, allow for a direct computation of the most probable realizations of extreme events that dominate turbulent statistics. Not only can it be shown that the extreme events predicted by instanton analysis actually appear in turbulent flows, but we can furthermore predict the tail scaling of PDFs of turbulent quantities.