I'll describe our recent efforts to characterize the spiking responses of a complete network of ON and OFF parasol ganglion cells in a small patch of primate retina, using a general linear model that consists of: (1) a linear receptive field that operates on the stimulus; (2) a feedback filter that captures the effects of the neuron's own spike history; (3) a set of cross-coupling filters that capture the effects of spiking in neighboring cells; and (4) an output nonlinearity that converts the total input to an instantaneous probability of spiking. The model is closely related to the more biophysically realistic integrate-and-fire model, and can exhibit a wide array of biologically relevant dynamical behaviors, such as refractoriness, spike rate adaptation, and bursting. We have applied the model to simultaneously-recorded responses of groups of macaque ON and OFF parasol retinal ganglion cells, stimulated with a 120-Hz spatiotemporal binary white noise stimulus. We find that the model accurately describes the stimulus-driven response (PSTH), and reproduces both the autocorrelations and pairwise cross-correlations of multi-cell responses. Finally, we show that the model can be used to map functional connectivity, providing a complete description of the identity, direction and form of functionally significant connections between cells.