By definition, vascular impedance is described in the frequency domain as the ratio of sinusoidal functions of pressure and flow, yielding spectral values of impedance modulus and phase. The impedance spectrum is determined by the structure and physical properties of the vascular system, such that for a given system the relation between pressure and flow can be modified by alteration of the geometric or mechanical properties of the vascular segments. Whereas input impedance of an arterial system can be readily determined by simultaneous measurement of just two time varying signals of blood pressure and flow, the production of the same impedance spectrum from the physical properties of the system would require information of inordinate complexity and magnitude. Hence, arterial models with a tractable number of parameters or explicit mathematical description are used to approximate the physiological impedance of a vascular structure, which in all animal species consists of distributed branching arterial networks. Although models are a necessary approximation, the strong similarity between the impedance spectra of models and physiological arterial systems enables investigations of fundamental concepts. This is illustrated by examining the effect of the branching structure on the decoupling of the high peripheral resistance from the ejecting ventricles and how physical parameters derived from the impedance spectrum can be used to investigate concepts of optimal design and features related to body size across a broad range of animal species.