Angiogenesis is a key prerequisite for growth in all vertebrate embryos and in many tumors. Rapid growth requires efficient transport of oxygen and metabolites. Hence, for a better understanding of tissue growth, biophysical properties of vascular systems, in addition to their molecular mechanisms, need to be investigated. The purpose of this article is twofold: (1) to discuss the biophysics of growing and perfused vascular systems in general, emphasizing non-sprouting angiogenesis and remodeling of vascular plexuses; and (2) to report on cellular details of sprouting angiogenesis in the initially non-perfused embryonic brain and spinal cord. It is concluded that (1) evolutionary optimization of the circulatory system corresponds to highly conserved vascular patterns and angiogenetic mechanisms; (2) deterministic and random processes contribute to both extraembryonic and central nervous system vascularization; (3) endothelial cells interact with a variety of periendothelial cells during angiogenesis and remodeling; and that (4) mathematical models integrating molecular, morphological and biophysical expertise improve our understanding of normal and pathological angiogenesis and account for allometric relations.