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For stable perception, we maintain mental representations of objects across space and time. What information is linked to such a representation? In this study, we extended our work showing that the spatiotemporal history of an object affects the way the object is attended the next time it is encountered. Observers conducted a visual search for a target among multiple distractors. Either the target location (Experiment 1) or the target feature (Experiment 2) could repeat from trial to trial. The entire visual search display was part of an object that could move in and out of view. Search was speeded when the target property repeated, but especially when the motion trajectory suggested that the same object had emerged. We show that this same-object benefit is tied to both the features and the spatial location of the target. It is most prominent for task-relevant features, but is weak to absent for task-irrelevant target features or …