The current state of heavy metal (HM) environmental pollution problems was considered in the review: the effects of HMs on the vital activity of plants and the functioning of their antioxidant system, including phenolic antioxidants. The latter performs an important function in the distribution and binding of metals, as well as HM detoxification in the plant organism. Much attention was focused on cadmium (Cd) ions as one of the most toxic elements for plants. The data on the accumulation of HMs, including Cd in the soil, the entry into plants, and the effect on their various physiological and biochemical processes (photosynthesis, respiration, transpiration, and water regime) were analyzed. Some aspects of HMs, including Cd, inactivation in plant tissues, and cell compartments, are considered, as well as the functioning of various metabolic pathways at the stage of the stress reaction of plant cells under the action of pollutants. The data on the effect of HMs on the antioxidant system of plants, the accumulation of low molecular weight phenolic bioantioxidants, and their role as ligand inactivators were summarized. The issues of polyphenol biosynthesis regulation under cadmium stress were considered. Understanding the physiological and biochemical role of low molecular antioxidants of phenolic nature under metal-induced stress is important in assessing the effect/aftereffect of Cd on various plant objects—the producers of these secondary metabolites are widely used for the health saving of the world’s population. This review reflects the latest achievements in the field of studying the influence of HMs, including Cd, on various physiological and biochemical processes of the plant organism and enriches our knowledge about the multifunctional role of polyphenols, as one of the most common secondary metabolites, in the formation of plant resistance and adaptation.