Cancerous tissue transformation developing usually over years or even decades of life is a highly complex process involving strong stressors damaging DNA, chronic inflammation, comprehensive interaction between relevant molecular pathways, and cellular cross-talk within the neighboring tissues. Only the minor part of all cancer cases are caused by inborn predisposition; the absolute majority carries a sporadic character based on modifiable risk factors which play a central role in cancer prevention. Amongst most promising candidates for dietary supplements are bioactive phytochemicals demonstrating strong anticancer effects. Abundant evidence has been collected for beneficial effects of flavonoids, carotenoids, phenolic acids, and organosulfur compounds affecting a number of cancer-related pathways. Phytochemicals may positively affect processes of cell signaling, cell cycle regulation, oxidative stress response, and inflammation. They can modulate non-coding RNAs, upregulate tumor suppressive miRNAs, and downregulate oncogenic miRNAs that synergically inhibits cancer cell growth and cancer stem cell self-renewal. Potential clinical utility of the phytochemicals is discussed providing examples for chemoprevention against and therapy for human breast cancer. Expert recommendations are provided in the context of preventive medicine.