Herein, I present an updated and contextualized literature review of functional genomic studies of natural phenols in the context of cancer. I suggest multilevel chemopreventive and anticancer mechanisms of action, which are shared by multiple dietary natural phenols. Specifically, I cite evidence that curcumin and resveratrol have multilevel anti-cancer effects through: (1) inducing either p53-dependent or p53-independent apoptosis in cancer cell lines, (2) acting as potent regulators of expression of oncogenic and anti-oncogenic microRNAs, and (3) inducing complex epigenetic changes that can switch off oncogenes/switch on anti-oncogenes. There is no simple reductionist explanation for anti-cancer effects of curcumin and resveratrol. More generally, multilevel models of chemoprevention are suggested for related natural phenols and flavonoids such as genistein, quercetin, or luteolin.