A previously viewed scene is often remembered as containing a larger extent of the background than was actually present, and information that was likely present just outside the boundaries of that view is often incorporated into the representation of that scene. This has been referred to as boundary extension. Methodologies used in studies on boundary extension (terminology, stimulus presentation, response measures) are described. Empirical findings regarding effects of characteristics of the stimulus (whether the stimulus depicts a scene, semantics of the scene, view angle, object size, object cropping, object orientation, object color, number of objects, depth of field, object distance, viewpoint production, scene orientation, motion, faces, emotions, modality, whether the scene is multimodal), characteristics of the display (aperture shape, aperture size, target duration, retention interval), and characteristics of the observer (allocation of attention, imagination, age, expectations and strategies, eye fixation, eye movements, monocular or binocular view, vantage point, confinement, prior exposure, expertise, arousal, pathology) on boundary extension are reviewed. Connections of boundary extension to other cognitive phenomena and processes (evolutionary adaptation, Gestalt principles, illusions, psychophysics, invariant physical principles, aesthetics, temporal boundary extension, normalization) are noted, and theories and theoretical considerations regarding boundary extension (multisource model, boundary transformation, mental imagery, 4E cognition, cognitive modularity, neurological mechanisms of scene representation) are discussed.