Mental representation of absent objects and events is a major cognitive achievement. Research is presented that explores how toddlers (2-to 3-year-old children) search for hidden objects and understand out-of-sight events. Younger children fail to use visually obvious cues, such as a barrier that blocks a moving object's path. Spatiotemporal information provided by movement cues directly connected to the hidden object is more helpful. A key problem for toddlers appears to be difficulty in representing a spatial array involving events with multiple elements.Keywords object search; reasoning; cognitive development; toddlers Representation of absent objects is a hallmark of cognition because it frees the organism from reliance on simply what is in sight at the moment. Tasks requiring search for hidden objects have been used to explore cognitive development since Piaget made it a critical feature of testing infants' representation of out-of-sight objects (Piaget, 1954). While it is easy to replicate Piaget's finding that infants will not search for a desired toy that has disappeared under a cloth, it has been hard to interpret this puzzling behavior. In his chapter in the Handbook of Child Psychology (1983), Paul Harris proposed that the reason for infants' failure in the Piagetian search task is not that they lack object permanence, but rather they do not know where to search for the hidden object. Eventually the infant overcomes this problem and knows to lift the cloth to find the toy.Knowing where to search for a hidden object depends on one's ability to use the cues that indicate where the hidden object is. For the 10-month-old in Piaget's search task, the cue is the place of disappearance. The infant sees the toy disappear under a cover, so under the cover is the obvious place to look. For the toddler, more complex cues can be used. In our lab we have tested toddlers' understanding of motion cues of disappearance and reappearance from behind multiple hiding sites, and the contact mechanical cue of a barrier. The movement cues are appreciated at a younger age, but the barrier cue is not used until around 3 years of age. What are the constraints that prevent a child from using readily available cues? Why does a child have difficulty in applying relevant knowledge to solve a problem? We will review research from our lab and seek some resolution to these problems in this chapter.First, let us describe the task. The child is seated in front of an apparatus that features a ramp and an opaque screen that can be placed to hide a large section of the ramp. Four doors cut into the screen can be opened to reveal a hiding place, and a barrier can be placed perpendicular to the ramp behind any of these doors. The barrier protrudes above the screen by several centimeters and stands out because it is painted a different color from the screen and the ramp.