Comprehensive studies of arterial pressure require understanding of the whole pressure waveform, not just the extremes of pressure (systolic and diastolic) in a peripheral artery. Such studies have been conducted in Sydney from the early 1960s and have been based on the concepts of steady state analysis, of vascular impedance, and of transfer function for pressure and flow in the frequency domain. These studies have emphasised the importance of wave reflection and have identified the cause of wave reflection, and shown how wave reflection can be modified. In the elderly and hypertensive, wave reflection returns early from peripheral sites, as a consequence of arterial stiffening, and boosts systolic pressure in the ascending aorta; this is responsible for "isolated systolic hypertension". Wave reflection in the upper limb causes the ill effects of arterial stiffening and the beneficial effects of vasodilator drugs to be underestimated. A new process, which combines the old technique of sphygmography with conventional sphygmomanometry, enables more precise evaluation of hypertensive subjects. Abnormal (early) wave reflection is a particular disadvantage in the presence of myocardial hypertrophy and impairment, and can explain development of cardiac failure. These concepts explain the favorable therapeutic effects of vasodilator drugs as being a consequence of reduction in wave reflection, as well as resulting from reduced peripheral resistance.