The neural coding problem --- deciding which stimuli will cause a given neuron to spike, and with what probability --- is a fundamental question in systems neuroscience. The high dimensionality of both stimuli and spike trains has spurred the development of a number of sophisticated statistical techniques for learning the neural code from finite experimental data. In particular, many recent studies aim to understand correlated spiking activity in neural populations, and to quantify how information is encoded in multi-neuronal spike reponses. We address this problem with data recorded from a complete mosaic of macaque parasol retinal ganglion cells in a small region of visual space. We find that a simple probabilistic spiking model with functional coupling between neurons captures both the stimulus dependence and the detailed spatiotemporal correlation structure of multi-neuronal responses. The functional coupling leads to changed estimates of the neurons' linear receptive fields (in particular, the overlap in the inferred receptive fields decreases) but, surprisingly, does not confer any advantage in predicting a single neuron's average response to repeated stimuli. However, we can use the model to make single-trial predictions of a given neuron's rate, and we find that ongoing network activity accounts for a significant portion of the trial-to-trial variability in a neuron's response. Finally, the probabilistic model allows us to assess the significance of correlated spiking by performing optimal Bayesian decoding of population spike responses; we find that approximately 15% more stimulus-related information is captured when correlations are taken into account. Joint work with E.J. Chichilnisky, J. Pillow, J. Shlens, E. Simoncelli, and V. Uzzell, at the Salk Institute, NYU, and the Gatsby Computational Neuroscience Unit.