Broken R Parity, Neutrino Anomalies and Collider Tests

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.