  The solar and atmospheric neutrino anomalies constitute the only solid and
most remarkable evidence for physics beyond the Standard Model, indicating that
the lepton mixing matrix is fundamentally distinct from that describing the
quarks. Here I will report on how supersymmetry with spontaneously or
bilinearly broken R Parity provides a predictive theory for neutrino mass and
mixing which leads to a solution of neutrino anomalies which can be clearly
tested at high energy accelerators.
