Excitatory-inhibitory neuronal networks arise in many neuronal systems. These include models for thalamocortical sleep rhythms, models for Parkinsonian rhythms and olfaction. Each of the models exhibits complex firing patterns. For example, experiments have demonstrated that neurons within a mammal's olfactory bulb or insect's antennal lobe produce complex firing patterns in response to an odor. The firing patterns may consist of epochs in which a subset of neurons fire synchronously. At each subsequent epoch, neurons drop in and drop out of the ensemble, giving rise to "dynamic clustering". In this talk, I will consider a general class of excitatory-inhibitory networks motivated by models for both Parkinsonian rhythms and olfaction. Geometric singular perturbation methods are used to reduce analysis of the models to a discrete-time dynamical system. The reduced model is then used to systematically characterize properties of the emergent firing patterns. and to determine how these properties depend on parameters including the underlying network architecture.