Modern experiments in nuclear and high-energy particle physics almost invariably use fast anticoincidence circuits to veto unwanted events. The desired events are typically accompanied by unwanted background processes that must be suppressed by enormous factors, ranging from thousands to many billions, to permit the desired signals to be detected and studied. Extreme examples of these kinds of experiments may be found at the Large Hadron Collider, where the enormous Atlas and CMS detectors must reject huge numbers of background events at very high rates, to isolate the very rare events being sought.