Isolated systolic hypertension (ISH) is present in the majority of persons who reach the age of 80 years, and is caused directly or indirectly by stiffening of the aorta and large central elastic arteries. Until recently, there was no consensus on whether or not persons over 80 should be treated, according to principles established for the younger group examined in the Systolic Hypertension in the Elderly Project (SHEP). The recent Hypertension in the Very Elderly Trial (HYVET) study endorses application of SHEP to most such subjects. This review describes the background to SHEP and HYVET, including concepts of hypertension and interpretation of blood pressure values. It describes the effects of age on arterial stiffness, and effects of stiffness on the heart, large arteries and microvessels in brain and kidneys as the basis of symptomatic disease. It describes logic of therapy with newer antihypertensives which indirectly affect arterial stiffness and form the basis of therapy in older persons. It proposes how, with what and in whom antihypertensive therapy could be offered in persons over age 80.