Here we demonstrate that the activity of neural ensembles can be quantitatively modeled. We first show that an ensemble dynamical model (EDM) accurately approximates the distribution of voltages and average firing rate per neuron of a population of simulated integrate-and-fire neurons. EDMs are high-dimensional nonlinear dynamical models. To faciliate the estimation of their parameters we present a dimensionality reduction method and study its performance with simulated data. We then introduce and evaluate a maximum-likelihood method to estimate connectivity parameters in networks of EDMS. Finally, we show that this model an methods accurately approximate the high-gamma power evoked by pure tones in the auditory cortex of rodents. Overall, this article demonstrates that quantitatively modeling brain activity at the ensemble level is indeed possible, and opens the way to understanding the computations performed by neural ensembles, which could revolutionarize our understanding of brain function.