There is a growing body of scientific research showing the link between depression and dementia in Alzheimer’s disease (AD). The chronic stress contributes to the formation of oxidative stress in the parts of the brain involved in the development of depression and AD. The scientific literature reports the significant role of antioxidants, which are highly effective in treating these diseases. In this review, we have summarized the relationship between chronic stress, oxidative stress, and the changes in the brain they cause occurring in the brain. Among all the compounds showing antioxidant properties, the most promising results in AD treatment were observed for Vitamin E, coenzyme Q10 (CoQ10), melatonin, polyphenols, curcumin, and selenium. In case of depression treatment, the greatest potential was observed in curcumin, zinc, selenium, vitamin E, and saffron.