One third of the burden of all the diseases in Europe is due to problems caused by diseases affecting brain. Although exceptional progress has been obtained for exploring it during the past decades, the brain is still terra-incognita and calls for specic research efforts to better understand its architecture and functioning.CoBCoM is our response to this great challenge of modern science with the overall goal to develop a joint Dynamical Structural-Functional Brain Connectivity Network (DSF-BCN) solidly grounded on advanced and integrated methods for diffusion Magnetic Resonance Imaging (dMRI) and Electro & Magneto-Encephalography (EEG & MEG).To take up this grand challenge and achieve new frontiers for brain connectivity mapping, we will develop a new generation of computational models and methods for identifying and characterizing the structural and functional connectivities that will be at the heart of the DSF-BCN. Our strategy is to break with the tradition to incrementally and separately contributing to structure or function and develop a global approach involving strong interactions between structural and functional connectivities. To solve the limited view of the brain provided just by one imaging modality, our models will be developed under a rigorous computational framework integrating complementary non invasive imaging modalities: dMRI, EEG and MEG.CoBCoM will push far forward the state-of-the-art in these modalities, developing innovative models and ground-breaking processing tools to provide in-fine a joint DSF-BCN solidly grounded on a detailed mapping of the brain connectivity, both in space and time.Capitalizing on the strengths of dMRI, MEG & EEG methodologies and building on the bio- physical and mathematical foundations of our new generation of computational models, CoBCoM will be applied to high-impact diseases, and its ground-breaking computational nature and added clinical value will open new perspectives in neuroimaging.