Antioxidant supplementation in the form of pills is thought to slow down the aging process through the "free radical" scavenger activity of these compounds. The idea arose from the "Free Radical Theory of Ageing" (FRTA), initially developed by Harman in 1956. In the present paper, we present some arguments against this theory. One of the most pertinent is that "free radicals", more properly renamed as reactive oxygen species (ROS), play important biological roles in defense mechanisms of the organism as illustrated, in particular, by the hormesis phenomenon. Surprisingly, a moderate production of ROS has been shown to extend the life span in animals.