Cancer is a multistep process involving genetic and epigenetic changes in the somatic genome. Genetic mutations as well as environmental factors lead to the initiation, promotion, and progression of cancer. Cancer progression ends in tumor metastasis to distant sites, and metastasis is the major reason for cancer patient deaths. Recent experimental evidence suggests the pivotal role of cancer stem cells. A tumor is heterogeneous and composed of different cell types. The cancer stem cells in the tumor have the capacity both to self-renew and differentiate to sustain the tumor. Features of cancer stem cells are described in this review, with an emphasis on the role that dietary phytochemicals may play in cancer chemoprevention. Ingredients in the diet can inhibit cancer cells and cancer stem cells. These compounds include curcumin from curry, epigallocatechin gallate from green tea, resveratrol from red wine, genistein from soy, sulforaphane from broccoli, and many others. Current research findings advocate the beneficial effects towards cancer chemoprevention via uptake of a combination of different dietary phytochemicals.