Anti-angiogenic therapies of solid cancers aim at specifically destroying the tumor vasculature in order to "asphyxiate" the tumors. Since few years, they represent a novel therapeutic tool, which allowed to significantly improve the survival of patients suffering from colon, breast, kidney and lung cancers. However, these therapies are limited in their efficacy by the appearance of tumor resistance phenomena. In this review, I describe the molecular and cellular mechanisms of tumor angiogenesis with a special focus on the important roles played by hypoxia, the endothelial growth factor VEGF and the endothelial tip-cells located at the extremity of sprouting neo-vessels. I present the factors that respectively control the activation phase and the maturation phase of angiogenesis, as well as their mechanisms of action. In a second part, the efficacy and the limits of anti-angiogenic therapies presently available on the market are described, and the recent elucidation of some molecular mechanisms of tumor resistance to anti-angiogenic therapies is reviewed.