Neuronal gamma-band synchronization is found in many cortical areas, is induced by different stimuli or tasks, and is related to several cognitive capacities. Thus, it appears as if many different gamma-band synchronization phenomena subserve many different functions. I argue that gamma-band synchronization is a fundamental process that subserves an elemental operation of cortical computation. Cortical computation unfolds in the interplay between neuronal dynamics and structural neuronal connectivity. A core motif of neuronal connectivity is convergence, which brings about both selectivity and invariance of neuronal responses. However, those core functions can be achieved simultaneously only if converging neuronal inputs are functionally segmented and if only one segment is selected at a time. This segmentation and selection can be elegantly achieved if structural connectivity interacts with neuronal synchronization. I propose that this process is at least one of the fundamental functions of gamma-band synchronization, which then subserves numerous higher cognitive functions.