<p>It is said that our visual experience is a ‘Grand Illusion’. Our brains can only process a fraction of the total information available in the natural world, and yet our subjective impression of that world appears richly detailed and complete. The apparent disparity between our conscious experience of the visual landscape and the precision of our internal representation has suggested to some that our brains are equipped with specialized mechanisms that surmount the inherent limitations of our perceptual and cognitive systems. One proposed set of mechanisms, called summary statistics, processes information in a scene by representing the regularities that are often shared among groups of similar in terms of descriptive statistics. For example, snowflakes blowing in the wind may be represented in terms of their mean direction and speed.</p> <p>Prevailing views hold that summary statistics may underlie all aspects of our subjective visual experience, inasmuch as such representations are thought to form automatically across multiple visual fields, exhaustively summarizing all available visual features regardless of attention. We challenge this view by showing that summary statistics are mediated by limited-capacity processes and therefore cannot unfold independently across multiple areas of the visual field. We also show that summary statistics require attention and thus cannot account for our sense of visual completeness outside attended visual space. In light of this evidence, we suggest that the application of summary representations to daily perceptual life has been overstated for the past decade. Indeed, many observations interpreted in terms of summary statistics can be accounted for by alternative cognitive processes, such as visual working memory.</p>