Angiogenesis has critical roles in normal vascular development and in important pathologies including cancer, wound healing and inflammation. This brief article will review the angiogenic response induced by the vascular permeability factor/vascular endothelial growth factor (VPF/VEGF) family of proteins and particularly VEGF-A, thought to be the single most important angiogenic factor. It will also review the steps and mechanisms by which VEGF-A induces the formation of new blood vessels and will provide an initial classification of the abnormal blood vessels that form in pathological angiogenesis. Finally, it will touch on the exciting relationships that are emerging between angiogenesis and the hemostatic and nervous systems.