In this note, recent results on the search for Gauge Mediated Supersymmetry Breaking (GMSB) and Anomaly Mediated Supersymmetry Breaking (AMSB) at the LEP and Tevatron colliders are summarized. We report on DZERO's search for GMSB in di-photon events with large missing transverse energy and discuss the sensitivity of similar searches based on future Tevatron integrated luminosities.