In many real-life systems, transient chaotic dynamics plays a major role. For instance, the chaotic spiral or scroll wave dynamics of electricaltextlessbrtextgreaterexcitation waves during life-threatening cardiac arrhythmias can terminate by itself. Epileptic seizures have recently been related to the collapse of transient chimera states. Controlling chaotic transients, either by maintaining the chaotic dynamics or by terminating it as quickly astextlessbrtextgreaterpossible, is often desired and sometimes even vital (as in the case of cardiac arrhythmias). We discuss in this study that the difference of thetextlessbrtextgreaterunderlying structures in state space between a chaotic attractor (persistent chaos) and a chaotic saddle (transient chaos) may have significanttextlessbrtextgreaterimplications for efficient control strategies in real life systems. In particular, we demonstrate that in the latter case, chaotic dynamics in spatially extended systems can be terminated via a relatively low number of (spatially and temporally) localized perturbations. We demonstratetextlessbrtextgreateras a proof of principle that control and targeting of high-dimensional systems exhibiting transient chaos can be achieved with exceptionallytextlessbrtextgreatersmall interactions with the system. This insight may impact future control strategies in real-life systems like cardiac arrhythmias.