Phenolic compounds or polyphenols are among the most common compounds of secondary metabolism in plants. Their biosynthesis is characteristic of all plant cells and is carried out with the participation of the shikimate and acetate-malonate pathways. In this case, polyphenols of various structures are formed, such as phenylpropanoids, flavonoids, and various oligomeric and polymeric compounds of phenolic nature. Their number already exceeds 10,000. The diversity of phenolics affects their biological activity and functional role. Most of their representatives are characterized by interaction with reactive oxygen species, which manifests itself not only in plants but also in the human body, where they enter through food chains. Having a high biological activity, phenolic compounds are successfully used as medicines and nutritional supplements for the health of the population. The accumulation and biosynthesis of polyphenols in plants depend on many factors, including physiological-biochemical, molecular-genetic, and environmental factors. In the review, we present the latest literature data on the structure of various classes of phenolic compounds, their antioxidant activity, and their biosynthesis, including their molecular genetic aspects (genes and transfactors). Since plants grow with significant environmental changes on the planet, their response to the action of abiotic factors (light, UV radiation, temperature, and heavy metals) at the level of accumulation and composition of these secondary metabolites, as well as their metabolic regulation, is considered. Information is given about plant polyphenols as important and necessary components of functional nutrition and pharmaceutically valuable substances for the health of the population. Proposals on promising areas of research and development in the field of plant polyphenols are presented.