Many years ago, Alex Comfort experimentally refuted Bidder's hypothesis that fish potentially were immortal. Later morphological and physiological studies, together with observations from fish populations in the wild, revealed that fish age in a way similar to that in other vertebrates. More recently, assessments of the age of fish have been revised, and have shown that some species live much longer than was estimated. These findings, together with the difficulties of demonstrating any increase in the rate of mortality with age in the long-lived, heavily exploited populations of fish, revived Bidder's ideas. I briefly review some of the more recent literature, and conclude that there is no evidence to suggest that fish are exceptional; like other vertebrates, sooner or later they grow old and die.