Very low diastolic blood pressure is known to be associated with increased cardiovascular risks. The risk of low systolic pressure, however, is disputed. This survey analyses the bulk of recent studies on this topic. In hypertensive individuals without comorbidity, neither a systolic nor a diastolic J curve could ever be detected. In contrast, in patients with coronary heart disease, diabetes, chronic kidney disease, or left ventricular hypertrophy, most studies document diastolic pressure < 70 mmHg (range 60-80 mmHg) as well as systolic pressure < 120 mmHg (range 110-130 mmHg) to be associated with increased cardiovascular morbidity and mortality. Data on primary prevention of stroke are inconsistent. A large secondary prevention study found a higher risk of recurrent stroke in old patients (> 75 years) with an in-study systolic pressure < 120 mmHg. Because the majority of studies in hypertensive patients show the optimal blood pressure to be 130-140/70-80 mmHg with a trend to higher values in old patients, there is no need for further lowering. Further decline of hitherto controlled blood pressure should prompt screening for an occult disease.