The control of visuospatial attention entails multiple processes, including both voluntary (endogenous) factors and stimulus-driven (exogenous) factors. Exogenous processes can be triggered by visual targets presented at a previously unattended location, thus capturing attention in a stimulus-driven manner. However, little is known about the relative role of stimulus salience and behavioral relevance for this type of spatial reorienting. Here, we directly assessed how salience and relevance affect activation of the frontoparietal attentional system, using either low-salience but task-relevant target stimuli or salient but task-irrelevant flickering checkerboards. We compared event-related functional magnetic resonance imaging responses for stimuli presented at the unattended versus attended side (invalid minus valid trials), separately for the 2 categories of visual stimuli. We found that task-relevant invalid targets activated the frontoparietal attentional network, demonstrating that this system engages when target stimuli are presented at an unattended location, even when these have a low perceptual salience. Conversely, the presentation of high-salience checkerboards in one hemifield while endogenous attention was engaged elsewhere did not activate the attentional network. These findings indicate that task relevance is critical for stimulus-driven engagement of the attentional network when attentional resources are endogenously allocated somewhere else.