An important feature of the living objects in distinction to the non-living matter is their ability to actively protect themselves from the uncontrolled oxidation. For this, living objects have a complex multi-component antioxidant system. The imbalance between the pro- and anti-oxidation processes in an organism leads to the development of a pathology named as an oxidative stress. This pathology is observed in many human and animal diseases of different origin and apparently it mediates the process of aging. Timely detection of oxidative stress enables to interrupt it and to prevent the development of undesirable consequences. This review focuses on the description of the components of the antioxidant system of an organism and of the new estimation methods of the effectiveness of antioxidant protection in tissues and organs.