Activated neuronal groups typically engage in rhythmic synchronization in the gamma-frequency range (30-100 Hz). Experimental and modeling studies demonstrate that each gamma cycle is framed by synchronized spiking of inhibitory interneurons. Here, we review evidence suggesting that the resulting rhythmic network inhibition interacts with excitatory input to pyramidal cells such that the more excited cells fire earlier in the gamma cycle. Thus, the amplitude of excitatory drive is recoded into phase values of discharges relative to the gamma cycle. This recoding enables transmission and read out of amplitude information within a single gamma cycle without requiring rate integration. Furthermore, variation of phase relations can be exploited to facilitate or inhibit exchange of information between oscillating cell assemblies. The gamma cycle could thus serve as a fundamental computational mechanism for the implementation of a temporal coding scheme that enables fast processing and flexible routing of activity, supporting fast selection and binding of distributed responses. This review is part of the INMED/TINS special issue Physiogenic and pathogenic oscillations: the beauty and the beast, based on presentations at the annual INMED/TINS symposium (http://inmednet.com).