  The principles of neural encoding and computations are inherently collective
and usually involve large populations of interacting neurons with highly
correlated activities. While theories of neural function have long recognized
the importance of collective effects in populations of neurons, only in the
past two decades has it become possible to record from many cells
simulatenously using advanced experimental techniques with single-spike
resolution, and to relate these correlations to function and behaviour. This
review focuses on the modeling and inference approaches that have been recently
developed to describe the correlated spiking activity of populations of
neurons. We cover a variety of models describing correlations between pairs of
neurons as well as between larger groups, synchronous or delayed in time, with
or without the explicit influence of the stimulus, and including or not latent
variables. We discuss the advantages and drawbacks or each method, as well as
the computational challenges related to their application to recordings of ever
larger populations.
