I propose that synchronization affects communication between neuronal groups. Gamma-band (30-90 Hz) synchronization modulates excitation rapidly enough that it escapes the following inhibition and activates postsynaptic neurons effectively. Synchronization also ensures that a presynaptic activation pattern arrives at postsynaptic neurons in a temporally coordinated manner. At a postsynaptic neuron, multiple presynaptic groups converge, e.g., representing different stimuli. If a stimulus is selected by attention, its neuronal representation shows stronger and higher-frequency gamma-band synchronization. Thereby, the attended stimulus representation selectively entrains postsynaptic neurons. The entrainment creates sequences of short excitation and longer inhibition that are coordinated between pre- and postsynaptic groups to transmit the attended representation and shut out competing inputs. The predominantly bottom-up-directed gamma-band influences are controlled by predominantly top-down-directed alpha-beta-band (8-20 Hz) influences. Attention itself samples stimuli at a 7-8 Hz theta rhythm. Thus, several rhythms and their interplay render neuronal communication effective, precise, and selective.