Antioxidants prevent cell damage from free radicals. Free radicals are unstable molecules created in the natural process of metabolism, and at an accelerated rate during exercise. Free radicals also form due to exposure from environmental sources such as cigarette smoke, air pollution or sunlight.

When it comes to antioxidants, they are not just purely beneficial:
https://www.dovepress.com/oxidative-stress-aging-and-diseases-peer-reviewed-fulltext-article-CIA
https://www.consumerreports.org/cro/2013/03/antioxidants-more-is-not-always-better/index.htm
https://joshmitteldorf.scienceblog.com/2012/11/19/anti-oxidants-a-disappointment-or-worse

Can you take tons of antioxidants, when some processes requires the presence of the reactive oxidant species in order to function? In other words, human body has evolved to include reactive oxygen species.

For example, growth is triggered by the presence of ROS, such as those that accumulate after heavy exercise. ROS signals the need for muscle growth and for additional mitochondria. Antioxidants consumed in large quantity can block this growth.

Antioxidants can improve exercise performance. ROS signals may end up being the same as the intensity of exercise may be greater.

There are many antioxidants, but ones that have been studied for supplementation include Vitamins, CoQ10, Polyphenols, Selenium, and Melatonin.

Vitamin C supplementation can have overall good health effects ^{1) 2)} when supplemented above the Dietary Reference Intake, but it reduces performance gains from exercising:
https://academic.oup.com/ajcn/article/87/1/142/4633311
https://www.ncbi.nlm.nih.gov/pubmed/19433800
https://www.ncbi.nlm.nih.gov/pubmed/22777327

Low levels of CoQ10 has been associated with disease. Oral administration of CoQ10 has been frequently administered in treatment resulting in mild to significant symptomatic improvement. ^{3) 4)}

Selenium dosage is sufficient through a healthy diet. Not enough or too high a dosage both lead to disease. An optimal dosage is still being researched. ⁵⁾

http://www.phdish.com/blog/antioxidants-and-aging
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2685276