Cancer growth is dependent on angiogenesis, the formation of new blood vessels, which represents a hallmark of cancer. Since this concept was established in the Seventies, inhibition of tumor development and metastases by blocking the neoangiogenic process has been an important approach to the treatment of tumors. However, antiangiogenic therapies are often administered when cancer has already progressed. The key to reducing the cancer burden is prevention. We noticed 20 years ago that a series of possible cancer chemopreventive agents showed antiangiogenic properties when tested in experimental models. This article reviews the relevant advances in the understanding of the rationale for targeting angiogenesis for cancer therapy and prevention and on substances with antiangiogenic activity that may be suitable for such strategies. Many compounds, either dietary derivatives or repurposed drugs, with antiangiogenic activity are possible tools for cancer angioprevention. Such molecules have a favorable safety profile and are likely to allow the prolonged duration necessary for an efficient preventive strategy. Recent evidence on mechanisms and possible use is described here for food derivatives, including flavonoids, retinoids, triterpenoids, omega fatty acids, and carotenoids from marine microorganisms. As examples, a number of compounds, including epigallocatechin, resveratrol, xanthohumol, hydroxytyrosol, curcumin, fenretinide, lycopene, fucoxanthin, and repurposed drugs, such as aspirin, β-blockers, renin–angiotensin–aldosterone inhibitors, carnitines, and biguanides are reviewed.