Severe durable changes may occur to the DNA structure caused by exogenous and endogenous risk factors initiating the process of carcinogenesis. By evidence, a large portion of malignancies have been demonstrated as being preventable. Moreover, the targeted prevention of cancer onset is possible, due to unique properties of plant bioactive compounds. Although genoprotective effects of phytochemicals have been well documented, there is an evident lack of articles which would systematically present the spectrum of anticancer effects by phytochemicals, plant extracts, and plant-derived diet applicable to stratified patient groups at the level of targeted primary (cancer development) and secondary (cancer progression and metastatic disease) prevention. Consequently, clinical implementation of knowledge accumulated in the area is still highly restricted. To stimulate coherent co-development of the dedicated plant bioactive compound investigation on one hand and comprehensive cancer preventive strategies on the other hand, the current paper highlights and deeply analyses relevant evidence available in the area. Key molecular mechanisms are presented to detail genoprotective and anticancer activities of plants and phytochemicals. Clinical implementation is discussed. Based on the presented evidence, advanced chemopreventive strategies in the context of 3P medicine are considered.