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Sharp wave-ripples (SWRs) are transient bursts of population activity generated in “off-line” states of the hippocampus. During SWRs, neuronal populations “replay” activity patterns observed during theta-gamma activity in the exploring animal. Our novel hippocampal slice preparation generates SWRs spontaneously, and this has allowed the characterization of the firing behavior and synaptic inputs of various cell types during SWR activity, as well as the direct measurement of the underlying cellular and synaptic parameters. We applied our recently developed software tool to systematically fit simplified models to these data, and built a large-scale model of the CA3 network. Then, using a combination of tools from physiology, pharmacology, optogenetics, and computer simulations, we investigated the mechanisms shaping in vitro SWRs. Our results suggest that the initiation of SWRs is governed by a combination of stochastic and refractory mechanisms, and requires the near-simultaneous activation of a critical number of pyramidal neurons. We also find that sharp wave-associated ripple oscillations in CA3 are generated by reciprocally connected parvalbumin-containing perisomatic interneurons when these cells are driven to fire at high frequencies. Importantly, models in which the efficacies of recurrent excitatory connections were uniform or varied randomly could not reproduce all of the experimentally measured characteristics of SWRs such as the low average firing rates of pyramidal cells. When we used spike-timing-dependent plasticity with simulated place cell activity during exploration to set up the strength of recurrent synapses, the model network produced spontaneous SWRs during which learned place cell sequences were replayed on a faster time scale, and the level of activity was also physiological. We then manipulated the synaptic weight matrix in various ways to reveal which aspects of its structure are critical in determining the stability of global activity levels, the emergence of coherent fast oscillations, and the generation of activity sequences. We concluded that the detailed structure of weights, as established during learning, is not only essential for the expression of meaningful neural representations, but is also a major determinant of population-level dynamics, and is, in particular, critical in producing the experimentally measured characteristics of SWRs.