Several studies have reported the health-beneficial effects of dietary phytochemicals, namely polyphenols, to prevent various diseases, including cancer. Polyphenols, like (-)-epigallocatechin-3-gallate (EGCG) from green tea, curcumin from turmeric, and ellagic acid from pomegranate are known to act by modulating antioxidant, anti-inflammatory and apoptotic signal transduction pathways in the tumor milieu. The evolving literature underscores the role of epigenetic regulation of genes associated with cancer by these polyphenols, primarily via non-coding RNAs (ncRNAs), such as microRNAs (miRNA) and long noncoding RNA (lncRNA). However, there is little clarity on the exact role(s) played by these ncRNAs and their interactions with other ncRNAs, or with their protein targets, in response to modulation by these dietary polyphenols. Here, we review ncRNA interactions and functional networks of the complex ncRNA interactome with their targets in preclinical studies along with the role of epigenetics as well as key aspects of pharmacokinetics and phytochemistry of dietary polyphenols. We also summarize the current state of clinical trials with these dietary polyphenols. Taken together, this synthetic review provides insights into the molecular aspects underlying the anticancer chemopreventive effects of dietary polyphenols as well as summarizes data on novel biomarkers modulated by these polyphenols for preventive or therapeutic purposes in various types of cancer.