Prevention is a promising option for the control of cancer. Cellular redox changes have emerged as a pivotal and proximal event in cancer. In this review, we provide a brief background on redox biochemistry, discuss the important distinction between redox signalling and oxidative stress, and outline the 'multiple biological personalities' of reactive oxygen and nitrogen species: at low concentrations they protect the cell; at higher concentrations they can damage many biological molecules, such as DNA, proteins, and lipids; and, as we argue here, they may also prevent cancer by initiating the death of the transformed cell. Nitric oxide-donating aspirin is discussed as an instructive example: it generates a state of oxidative stress through which it affects several redox-sensitive signalling pathways, leading ultimately to the elimination of the neoplastic cell via apoptosis or necrosis. As additional examples, we discuss the chemopreventive n-3 polyunsaturated fatty acids and conventional nonsteroidal anti-inflammatory drugs, which induce cell death through redox changes. We conclude that modulation of redox biochemistry represents a fruitful approach to cancer prevention.