Angiogenesis is a biological process by which new capillaries are formed from pre-existing vessels. It occurs in both physiological conditions such as embryo development, cyclically in the female genital system and during wound repair, and pathological conditions, such as arthritis, diabetic retinopathy and tumors. In solid tumor growth, a specific critical turning point is the transition from the avascular to the vascular phase. Having developed an intrinsic vascular network, the neoplastic mass is able to grow indefinitely (unlike all the other forms, tumor angiogenesis is not limited in time) both in situ and at distant sites (metastasis) in so far as an intrinsic vascular network enables its cells to enter the vascular bed and colonize other organs. Tumor angiogenesis depends mainly on the release by neoplastic cells of growth factors specific for endothelial cells and able to stimulate growth of the host's blood vessels. This review describes its history as traced by the main contributions to the international medical literature and their contents. The specific new paradigm discussed here has been gaining general approval and considerable confirmation, thanks to its possible applications, as recently highlighted by the introduction of anti-angiogenic substances in adjuvant tumor management.