In ischemic stroke, positron-emission tomography (PET) established the imaging-based concept of penumbra. It defines hypoperfused, but functionally impaired, tissue with preserved viability that can be rescued by timely reperfusion. Diffusion-weighted and perfusion-weighted (PW) magnetic resonance imaging (MRI) translated the concept of penumbra to the concept of mismatch. However, the use of mismatch-based patient stratification for reperfusion therapy remains a matter of debate. The equivalence of mismatch and penumbra, as well as the validity of the classical mismatch concept is questioned for several reasons. First, methodological differences between PET and MRI lead to different definitions of the tissue at risk. Second, the mismatch concept is still poorly standardized among imaging facilities causing relevant variability in stroke research. Third, relevant conceptual issues (e.g., the choice of the adequate perfusion measure, the best quantitative approach to perfusion maps, and the required size of the mismatch) need further refinement. Fourth, the use of single thresholds does not account for the physiological heterogeneity of the penumbra and probabilistic approaches may be more promising. The implementation of this current knowledge into an optimized state-of-the-art mismatch model and its validation in clinical stroke studies remains a major challenge for future stroke research.