  Neurons in the brain represent information in their collective activity. The
fidelity of this neural population code depends on whether and how variability
in the response of one neuron is shared with other neurons. Two decades of
studies have investigated the influence of these noise correlations on the
properties of neural coding. We provide an overview of the theoretical
developments on the topic. Using simple, qualitative and general arguments, we
discuss, categorize, and relate the various published results. We emphasize the
relevance of the fine structure of noise correlation, and we present a new
approach to the issue. Throughout we emphasize a geometrical picture of how
noise correlations impact the neural code.
