Forty years ago, Judah Folkman predicted that tumor growth is dependent on angiogenesis and that inhibiting this process might be a new strategy for cancer therapy. This hypothesis formed the foundation of a new field of research that represents an excellent example of how a groundbreaking scientific discovery can be translated to yield benefits for patients. Today, antiangiogenic drugs are used to treat human cancers and retinal vascular diseases. Here, we guide readers through 40 years of angiogenesis research and discuss challenges of antiangiogenic therapy.