  Precision studies of QCD at $e^+e^-$ 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 (${\cal O}(\alpha_s^3)$) to three-jet
production and related event shapes, and discuss their phenomenological impact.
