The study of antipredator vigilance underwent a rapid and relatively recent synthesis 15-20 years ago. During the rise of behavioral ecology and sociobiology, researchers began to measure how often animals looked up from feeding. Subsequently, the field of vigilance crystallized quickly around a few striking results and an elegant theory. The convenient mathematical assumptions of this original theory continue to channel researchers' attentions today. Although data tend to match these assumptions - flock members scan independently, vigilance sequences are essentially unpredictable, and interscan intervals are highly variable - the assumptions themselves are difficult to justify. Some of our basic ideas about vigilance require detailed re-examination.