Hypertension (systolic/diastolic blood pressure [SBP/DBP] ≥140 and/or ≥90 mmHg) is a very common condition in older people (prevalence >60%) and one of the leading causes of death and disability worldwide. The cardiovascular, cerebrovascular, and renal benefits of treating it properly are abundantly supported by clinical trials. However, an excessive reduction in BP (e.g., postural or pharmacological), especially if it is sustained over time, is less known but apparently more frequent than expected and clinically-efficient to detect (e.g., with ambulatory monitoring [ABPM] or home-BP self-measurement). Some studies have associated hypotension with a greater risk of fatigue, dizziness, imbalance, falls, cardiovascular disease, kidney damage, and dementia. In older and frail patients with treated hypertension, some proposed safety margins are SBP/DBP of 130-139 (if tolerated)/70-79 mmHg and, in general, BP should not be reduced below these values. Orthostatic hypotension (>20/10 mmHg fall in SBP/DBP within 3 minutes of erect standing) and ambulatory hypotension (mean daytime BP <110/70 mmHg) can be detected measuring standing BP in the office and with 24-hour ABPM, respectively. Several studies suggest that there may not be a single treatment goal for all patients because the BP/outcome relation seems to be modified by the patient’s age, co-morbidities, drugs, etc., and ignorance of this can lead to hypotension and other deleterious effects. The balance between efficacy and safety of the drug treatment of hypertension can be reasonably achieved by the good doctor practicing personalized medicine, individualizing the treatment of each of his older patients (who are genetic, demographic, physiological, metabolic, psychological, and culturally different), combining the updated scientific evidence, his/her experience and comprehensive knowledge of the patient (age, co-morbidities, etc), and the preferences of the patient or their caregiver. Most of this review is supported by some recent clinical practice guidelines.