  Precision studies of QCD at electron-positron colliders are based on
measurements of event shapes and jet rates. To match the high experimental
accuracy, theoretical predictions to next-to-next-to-leading order (NNLO) in
QCD are needed for a reliable interpretation of the data. We report the first
calculation of NNLO corrections O(alpha_s^3) to three-jet production and
related event shapes, and discuss their phenomenological impact.
