Phytochemicals are potential cancer chemopreventive agents, based partly on cellular research establishing that phytochemicals inhibit the proliferation of cancer cells. To elucidate the mechanism of phytochemicals, a basic understanding is needed of what stimulates cancer cell proliferation. Cancer cells, particularly those that are highly invasive or metastatic, may require a certain level of oxidative stress to maintain a balance between undergoing either proliferation or apoptosis. They constitutively generate large but tolerable amounts of H2O2 that apparently function as signaling molecules in the mitogen-activated protein kinase pathway to constantly activate redox-sensitive transcription factors and responsive genes that are involved in the survival of cancer cells as well as their proliferation. With such a reliance of cancer cells on H2O2 it follows that if the excess H2O2 can be scavenged by phenolic phytochemicals having antioxidant activity, the oxidative stress-responsive genes can be suppressed and consequently cancer cell proliferation inhibited. On the other hand, phenolic phytochemicals and another group of phytochemicals known as isothiocyanates can induce the formation of H2O2 to achieve an intolerable level of high oxidative stress in cancer cells. As an early response, the stress genes are activated. However, when the critical threshold for cancer cells to cope with the induced oxidative stress has been reached, key cellular components such as DNA are damaged irreparably. In conjunction, genes involved in initiating cell cycle arrest and/or apoptosis are activated. Therefore, phytochemicals can either scavenge the constitutive H2O2 or paradoxically generate additional amounts of H2O2 to inhibit the proliferation of cancer cells.