Theta and gamma oscillations are believed to organise hippocampal activity and function. The current dominant view posits the existence of two gamma frequency sub-bands, occurring at different theta phases in CA1, produced by different generators and sub-serving exclusive cognitive operations. Such views are however grounded on averaging over many oscillatory events. Here, we explore agnostically the diversity of individual theta-gamma bursts and find, in striking contrast with the discrete sub-bands hypothesis, that gamma bursts with nearly every combination of frequency, amplitude and theta-phase can occur in every CA1 layer. Average oscillatory spectra reflect indeed only a minority of strong power events, overshadowing pervasive diversity. In other words, averages don’t exist. Is this oscillatory diversity to be expected or not? To answer this first question, we constructed a spiking computational model of local recurrent circuitry, involving one excitatory and one inhibitory (fast-spiking-like) population. We reveal then that, for most parameter combinations, complex oscillations fluctuating over the entire gamma spectrum arise, as observed in data, without need for any fine tuning. Second, is this diversity functional or not? To probe whether theta-gamma variability reflects noise or, on the contrary, extractable information about behavior, we used a machine learning approach to decode from individual theta-gamma oscillatory bursts the running speed and the coarse position of mice navigating in a maze to seek for reward. We found that behavioral features can be decoded with large, above chance-level accuracy in all probed hippocampal layers. Furthermore, different “styles of complexity” are observed for different layers, as well as for different stages of task learning. Altogether, our findings suggest that hippocampal oscillatory diversity is not mere noise but carries an actual encoding of context and behavior. These hippocampal oscillatory codes are complex in nature and not reducible to simpler descriptions in terms of a few reference bands.