Growing evidence has been accumulated to show the anticancer effects of daily consumption of polyphenols. These dietary polyphenols include chlorogenic acid, curcumin, epigallocatechin-3-O-gallate, genistein, quercetin, and resveratrol. These polyphenols have similar chemical and biological properties in that they can act as antioxidants and exert the anticancer effects via cell signaling pathways involving their reactive oxygen species (ROS)-scavenging activity. These polyphenols may also act as pro-oxidants under certain conditions, especially at high concentrations. Epigenetic modifications, including dysregulation of noncoding RNAs (ncRNAs) such as microRNAs, long noncoding RNAs, and circular RNAs are now known to be involved in the anticancer effects of polyphenols. These polyphenols can modulate the expression/activity of the component molecules in ROS-scavenger-triggered anticancer pathways (RSTAPs) by increasing the expression of tumor-suppressive ncRNAs and decreasing the expression of oncogenic ncRNAs in general. Multiple ncRNAs are similarly modulated by multiple polyphenols. Many of the targets of ncRNAs affected by these polyphenols are components of RSTAPs. Therefore, ncRNA modulation may enhance the anticancer effects of polyphenols via RSTAPs in an additive or synergistic manner, although other mechanisms may be operating as well.