Simultaneous recordings from large neural populations are becoming increasingly common. Correlations in neural activity measured in such recordings can reveal important aspects of neural network organization and function. However, estimating and interpreting large correlation matrices is challenging. Moreover, the network mechanisms that modulate these changes are also not fully understood. I will discuss how estimation of correlations can be improved by regularization, i.e. by imposing a structure on the estimate. I will illustrate this approach by analyzing the activity of 150–350 cells in mouse visual cortex. I will show that activity in this network is best explained by a combination of a sparse graph of pairwise partial correlations representing local interactions, and a low-rank component representing common fluctuations and external inputs. Correlated activity can also be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. I will review recent theoretical results that identify three separate biophysical mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations, and the transfer function of single neurons. Along with the statistical approaches discussed in the first part of the talk, such mechanistic constraints on the modulation of population activity will be important in analyses of high dimensional neural data.