The only treatment that has been proven to improve outcome after ischemic stroke is to reperfuse the brain by removing the arterial obstruction. All animal and clinical studies show that brain tissue exposed to the reduced blood flow inherent after an arterial occlusion dies quickly, in proportion to the reduction of flow. Brain tissue where there is the most profound reduction of flow (the ischemic “core”) dies within minutes. In areas where flow is less severely reduced (the ischemic “penumbra”), tissue death occurs more gradually, dependent on the adequacy of collateral flow. The faster that normal flow can be re-established, the less tissue death and the less consequent disability occurs. This chapter deals with systemic thrombolysis.