It is well established by a large number of randomized controlled trials that lowering blood pressure (BP) and low-density lipoprotein cholesterol (LDL-C) by drugs are powerful means to reduce stroke incidence, but the optimal BP and LDL-C levels to be achieved are largely uncertain. Concerning BP targets, two hypotheses are being confronted: first, the lower the BP, the better the treatment outcome, and second, the hypothesis that too low BP values are accompanied by a lower benefit and even higher risk. It is also unknown whether BP lowering and LDL-C lowering have additive beneficial effects for the primary and secondary prevention of stroke, and whether these treatments can prevent cognitive decline after stroke.