SUMMARY Vascular networks refer here mainly to the microscale capillary networks of the vascular system of mammals, although they may also be considered to include the small arteries that feed the capillaries and the small veins that drain them. The modeling of these networks for resting mammals is reviewed within the context of describing related scaling laws for mammals of vastly different size. Basic processes are considered and alternative approaches mentioned. All lead to the same scaling laws for the radius, length and number of the vessels. The applicability of the relations is illustrated using existing measurements. Discussion is also included on the effect of strenuous exercise on the scaling law for number of capillary vessels and matters related to it.