Oxidative stress is a phenomenon associated with imbalance between production of free radicals and reactive metabolites (e.g. superoxide and hydrogen peroxide) and the antioxidant defences. Oxidative stress in individuals with Down syndrome (DS) has been associated with trisomy of the 21st chromosome resulting in DS phenotype as well as with various morphological abnormalities, immune disorders, intellectual disability, premature aging and other biochemical abnormalities. Trisomy 21 in patients with DS results in increased activity of an important antioxidant enzyme Cu/Zn superoxide dismutase (SOD) which gene is located on the 21st chromosome along with other proteins such as transcription factor Ets-2, stress inducing factors (DSCR1) and precursor of beta-amyloid protein responsible for the formation of amyloid plaques in Alzheimer disease. Mentioned proteins are involved in the management of mitochondrial function, thereby promoting mitochondrial theory of aging also in people with DS. In defence against toxic effects of free radicals and their metabolites organism has built antioxidant defence systems. Their lack and reduced function increases oxidative stress resulting in disruption of the structure of important biomolecules, such as proteins, lipids and nucleic acids. This leads to their dysfunctions affecting pathophysiology of organs and the whole organism. This paper examines the impact of antioxidant interventions as well as positive effect of physical exercise on cognitive and learning disabilities of individuals with DS. Potential therapeutic targets on the molecular level (oxidative stress markers, gene for DYRK1A, neutrophic factor BDNF) after intervention of natural polyphenols are also discussed.