Cancer is a serious group of diseases that is a huge problem on a global scale and is the second most common cause of death. Commonly used therapies do not always lead to the complete elimination of diseased cells or tissues and are also burdened with side effects that reduce the quality of life of patients. Due to these difficulties, new therapeutic approaches are still being sought. In recent years, there has been a return to interest in natural methods of treating various diseases, among which phytochemicals are particularly interesting. This article reviews plant extracts with anticancer properties with different mechanisms of action (proapoptotic, antiproliferative, antiangiogenic, immunomodulatory). In addition, plant extracts that reduce the side effects of chemotherapy and the limitations and prospects for the use of plant extracts in anticancer therapy are described. Our goal was to create an up-to-date information base that would encourage scientists to intensify research into supplementing targeted anticancer therapies with additional protective and preventive measures, in which natural mixtures of phytochemicals (plant extracts) are effective allies. At the same time, we encourage discussion on the limitations of their use in light of the orthodox principles of classical medicine and pharmacy (issues of safety, quality, drug purity, and dose precision), which are a priori correct but have not yet led to the elimination of cancer from the group of incurable diseases.