We are all familiar with the correlation coefficient between two sets of numbers. Now suppose we replace the numbers by vector-valued images in any number of dimensions. The correlation random field is the ’image’ of correlations at all possible pairs of points in the two images. We use random field theory to set a threshold on the correlations so that those above the threshold are statistically significant, corrected for searching over all pairs of points. We apply this idea to resting state networks of fMRI images of brain activity, and networks of connectivity in cortical thickness.