BOLD fMRI is currently the mainstay of neuroimaging in cognitive neuroscience. Advances in scanner technology, image acquisition protocols, experimental design, and analysis methods promise to push forward fMRI from mere cartography to the true study of brain organization. However, fundamental questions concerning the interpretation of fMRI data abound, as the conclusions drawn often ignore the actual limitations of the method.  Among others are often the misinterpretation of connectivity patterns relying on electrical stimulation of brain structures, of cortical-layer-dependent activations obtained by measurements of blood flow or volume changes, or of up and down signal-modulations induced by neuromodulation rather than sensory-stimulus or task.   In my talk, I shall describe our current understanding of the neurophysiological and hemodynamic signals, the structural and functional neurovascular coupling, and the constraints of DES-fMRI in studies of connectivity.