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. This talk discusses a few crucial points about fMRI connectivity analysis: i) Model selection procedures for connectivity and the structural graph models that are considered, ii) Temporal precedence in dynamic models of connectivity and causality concepts based on it, such as Wiener/Granger causality iii) The effects of hemodynamics on fMRI connectivity measures and the incorporation of those effects in deconvolution approaches.