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Functional magnetic resonance imaging (fMRI) is increasingly used to study functional connectivity in large-scale brain networks that support cognitive and perceptual processes. We face serious conceptual, statistical and data analysis challenges when addressing the combinatorial explosion of possible interactions within high-dimensional fMRI data. Moreover, we need to know, and account for, the physiological mechanisms underlying our signals. We argue here that (i) model selection procedures for connectivity should include consideration of more than just a few brain structures, (ii) temporal precedence - and causality concepts based on it - are essential in dynamic models of connectivity and (iii) undoing the effect of hemodynamics on fMRI data (by deconvolution) can be an important tool. However, it is crucially dependent upon assumptions that need to be verified.