Why do we perceive objects? Visual perception starts with localized filters that subdivide the image into fragments that undergo separate analyses. Our visual system has to reconstruct the objects that surround us. It has to bind image fragments of the same object and to segregate them from other objects and the background. The standard view in psychology is that perceptual grouping is achieved by a parallel, pre-attentive process that relies on Gestalt grouping cues. My work has started to challenge this view by demonstrating that the visual cortex also implements a serial, attention-demanding algorithm for perceptual grouping. This grouping process may represent the first serial brain algorithm that can be understood at the psychological, neurophysiological and computational level. The present proposal therefore has the potential to revolutionize our view of visual cognition.Understanding feature binding would represent a breakthrough in cognitive neuroscience. Different brain areas represent distinct visual features. How is activity in these areas integrated? We propose that perceptual grouping relies on two complementary processes, “base-grouping” and “incremental grouping”. We hypothesize that base-grouping is pre-attentive and relies on feed-forward connections from lower to higher areas that activate neurons and determine their stimulus selectivity. In contrast, we propose that incremental grouping relies on feedback and horizontal connections, which propagate enhanced neuronal activity to highlight all the features that belong to the same perceptual object. The present proposal will determine the role of attention in feature binding, the interactions between brain areas for grouping with fMRI in humans and with electrophysiology in non-human primates to reveal the algorithms for perceptual grouping as they are implemented in our brains.