Physical training is known to induce a biochemical adaptive response which might require an increase in the ingestion and/or the absorption of micronutrients. A question that is still being raised is whether acute or chronic exercise modifies antioxidant requirements. First, the present review brings to light the most crucial studies on the topic. Second, it interprets the established relationships between antioxidant micronutrient intakes and the adaptive response of antioxidant systems. Finally, it exposes the major questions connected with antioxidant micronutrient requirements for athletes. To this effect, the training-load interaction with nutrition is taken into account. As oxidative stress cannot be avoided, the imbalance between oxidants and antioxidants can be alleviated to minimise oxidative damage and outcomes. There is growing evidence that one specific antioxidant cannot by itself prevent oxidative stress-induced damage, as direct adverse effects of supplementation are attributed to undesirable synergic effects. Other effects can be supposed that limit the endogenous adaptive effect of training. High doses of antioxidant supplements can minimise the effects of radical oxygen species themselves or generate pro-oxidant effects. Effects are only exhibited when nutritional status is deficient. There are no convincing effects of supplementation in well-trained athletes. Risk/benefit analysis emerges on evidence for an unknown risk of supranutritional intakes, a supposed impairment of adaptive effects and a still unknown long-term risk. Appropriate status can be achieved by a diversified and balanced diet, adapted to specific needs, by awareness of high-density food intakes (avoiding products containing a low density of micronutrients).