In a curve-tracing task, subjects have to judge whether items are located on a single, continuous curve. Spatially separate segments of such a curve are related to each other through grouping criteria, like collinearity and connectedness. These grouping cues need to be exploited during curve tracing, but it is still an open issue how grouping of contour segments is achieved by the visual system. Many contemporary theories of visual perception assume that grouping operations are carried out pre-attentively, with unlimited capacity. The present study examines this assumption by investigating the involvement of attention in curve tracing. The results show that attention is directed to contour segments that need to be grouped together. The distribution of attention is guided by grouping criteria, such as connectedness. Apparently, attention is required to group spatially separate contour segments into a coherent representation of a curve.