Correlated activity in populations of neurons has been observed in many brain regions and plays a central role in cortical coding, attention, and network dynamics. Accurately quantifying neuronal correlations presents several difficulties. For example, despite recent advances in multicellular recording techniques, the number of neurons from which spiking activity can be simultaneously recorded remains orders magnitude smaller than the size of local networks. In addition, there is a lack of consensus on the distribution of pairwise spike cross correlations obtained in extracellular multi-unit recordings. These challenges highlight the need for theoretical and computational approaches to understand how correlations emerge and to decipher their functional role in the brain.