Investigations of visual crowding, where a target is difficult to identify because of flanking elements, has largely used a theoretical perspective based on local interactions where flanking elements pool with or substitute for properties of the target. This successful theoretical approach has motivated a wide variety of empirical investigations to identify mechanisms that cause crowding, and it has suggested practical applications to mitigate crowding effects. However, this theoretical approach has been unable to account for a parallel set of findings that crowding is influenced by long-range perceptual grouping effects. When the target and flankers are perceived as part of separate visual groups, crowding tends to be quite weak. Here, we describe how theoretical mechanisms for grouping and segmentation in cortical neural circuits can account for a wide variety of these long-range grouping effects. Building on previous work, we explain how crowding occurs in the model and explain how grouping in the model involves connected boundary signals that represent a key aspect of visual information. We then introduce new circuits that allow nonspecific top-down selection signals to flow along connected boundaries or within a surface contained by boundaries and thereby induce a segmentation that can separate the visual information corresponding to the flankers from the visual information corresponding to the target. When such segmentation occurs, crowding is shown to be weak. We compare the model's behavior to 5 sets of experimental findings on visual crowding and show that the model does a good job explaining the key empirical findings.