Research studies on hypertension have, so far, generally focused on vascular resistance and small arteries. The high prevalence of systolic hypertension in patients older than 50 years and the development of noninvasive Doppler and echotracking techniques have made it possible to determine large-artery stiffness with a high degree of reproducibility. Increased arterial stiffness and disturbed wave reflections are the basis for understanding reduced aortic elasticity and systolic hypertension, particularly in older people. This hemodynamic pattern results from mechanical factors and other pressure-independent risk factors, such as diabetes mellitus, renal failure, obesity and severe atherosclerosis. Distinct phenotypes of arterial stiffness and pulse pressure result from specific gene polymorphisms, such as those related to the renin-angiotensin system. The roles of arterial stiffness and wave reflections in hypertension have been elucidated by modern interpretations of the blood-pressure curve in relation to its propagation, mechanisms of systolic-blood-pressure amplification, and the pulse-pressure amplitude. New predictors of cardiovascular risk have been identified, such as increased pulse pressure and pulse-wave velocity, and disturbed wave reflections, all of which are independent predictors of cardiovascular risk that are more powerful than either systolic or diastolic blood pressure alone. Therapeutic trials are investigating ways to reduce stiffness, and thereby allow the selective reduction of systolic and pulse pressure in hypertensive patients with or without advanced renal failure. Modern pharmacologic agents need to be identified, which could reduce systolic hypertension in patients older than 50 years. Here we discuss the structural and functional factors that influence arterial stiffness, wave reflections and pulse pressure in hypertension, as well as their related roles in cardiovascular risk.