In the last decade, the possibility to noninvasively estimate cortical activity and connectivity has been highlighted by the application of the techniques known as high resolution EEG. These techniques include a subject's multi-compartment head model (scalp, skull, dura mater, cortex) constructed from individual magnetic resonance images, multi-dipole source model, and regularized linear inverse source estimates of cortical current density. More recently, it has proved as the use of information from the hemodynamic responses of the cortical areas as revealed by block-designed (strength of activated voxels) fMRI improves dramatically the estimates of cortical activity and connectivity. Here, we present some applications of such estimation in two set of high resolution EEG and fMRI data, related to the motor (finger tapping) and cognitive (Stroop) tasks. We observed that the proposed technology was able to unveil the direction of the information flow between the cortical regions of interest.