The ischemic penumbra was initially defined by Symon, Lassen and colleagues in the 1970s as an area of brain tissue with inadequate blood flow to maintain electric activity of neurons but adequate blood flow to preserve the function of the ion channels. This area of tissue, receiving enough blood to survive but not enough to function, often surrounds or abuts the irreversibly damaged core in ischemic stroke. It was shown that if blood flow could be restored to this area of marginal perfusion, the tissue could survive and function again, and growth of the core could be prevented. Based on seminal PET studies, penumbra or "penumbral tissue" eventually took on a subtly different meaning - the area of brain that is destined to progress to infarct unless blood flow is restored within a particular time window. The penumbra thus became the target for all acute stroke interventions - to preserve viability of the tissue and restore function. New imaging techniques, including diffusion and perfusion MRI and CT perfusion, were developed to rapidly identify individuals with penumbra, who were thought to be the best candidates for aggressive interventions to restore blood flow, particularly beyond the licensed time-window for IV thrombolysis. However, most clinical trials have failed to establish the usefulness of identifying candidates for treatment in this way using pre-specified protocols and primary endpoints. These trials have used different and sometimes unvalidated thresholds of hypoperfusion as well as irreversible infarct and various definitions of significant penumbra (or mismatch between irreversible infarct and hypoperfused, but salvageable tissue), and reanalysis of their data using more refined image processing showed post-hoc positivity. They have also evaluated outcome in a variety of ways, with few studies measuring the direct effect of restoring blood flow on the function of the penumbral tissue. Therefore, important remaining questions include how to define, characterize, and image the penumbra in acute stroke to achieve the greatest reliability and validity for what we want to measure, and whether this concept, so defined, provides an optimal target for stroke therapy using state-of-the-art trial design.