One of the central tenets of systems neuroscience is that tuning curves are a byproduct of the interactions between neurons. Using multi-electrode recordings and recently developed inference techniques we can begin to examine this idea in detail and study how well we can explain the functional properties of neurons using the activity of other simultaneously recorded neurons. Here we examine datasets from 6 different brain areas recorded during typical sensorimotor tasks each with ~100 simultaneously recorded neurons. Using these datasets we measured the extent to which interactions between neurons can explain the tuning properties of individual neurons. We found that, in almost all areas, modeling interactions between 30-50 neurons allows more accurate spike prediction than tuning curves. This suggests that tuning can, in some sense, be explained by interactions between neurons in a variety of brain areas, even when recordings consist of relatively small numbers of neurons.