Many perfusion-related MRI parameters are used to investigate the penumbra in stroke. Although time-to-maximum (Tmax) of the residue function has been suggested as a very promising parameter, its physiological meaning and sensitivity to experimental conditions are not well-understood. We used simulations to further our understanding of the practical meaning of Tmax and to provide recommendations for its use in clinical investigations. We interpret in vivo examples guided by the simulation findings. Whereas Tmax has several attractive properties for clinical use, it is shown that its physiological interpretation is complex and affected by experimental conditions. Tmax is found to reflect a combination of delay, dispersion, and, to a lesser degree, mean transit time. It should therefore mainly be considered a measure of macrovascular characteristics. Furthermore, based on the simulations, use of temporal-interpolation is highly recommended, as is correction for slice-acquisition timing differences. Special care should be taken when setting-up Tmax thresholds for data acquired with different protocols (eg, multicenter studies) because various factors can influence the measured Tmax. Because of its complementary information, used in conjunction with delay-insensitive cerebral blood-flow, cerebral blood volume, and mean transit time maps, Tmax should provide important additional information on brain hemodynamic status.