In treatment of hypertension not only the pressure response is of interest, but also the effect on arterial parameters, for example, stiffness and resistance, is essential. We therefore reviewed what quantitative information on arterial stiffness can be obtained from pressure wave analysis. Using data from published large cohort studies, we derived relations between stiffness and the pressure-derived variables systolic pressure, pulse pressure, augmentation index (AIx), return time of reflected wave and reflection magnitude. All pressure-derived variables give limited information on arterial function in terms of stiffness and resistance, except AIx (in low stiffness range only). Input impedance as a comprehensive description of the arterial system is too complex to derive and interpret in practice, but is accurately described by three parameters: systemic vascular resistance, total arterial stiffness, and aortic characteristic impedance (outflow tract size and proximal aortic stiffness). These parameters predict aortic pressure well in terms of magnitude and shape: with measured flow the predicted (p) and measured (m) systolic, Ps, and diastolic, Pd pressures relate as Ps,p=0.997 Ps,m-1.63 and Pd,p=1.03 Pd,m-3.12  mmHg (n=17). Therefore, methods should be developed to determine, preferably noninvasively, these three arterial parameters. Variables derived from pressure wave shape alone (e.g. inflection point, AIx among others), and wave separation (e.g. reflection magnitude), while predicting cardiovascular events, give little information on arterial function. We propose to develop new, and improve existing, noninvasive methods to determine systemic vascular resistance, total arterial stiffness, and aortic characteristic impedance. This will allow quantifying the response of arterial function to treatment.