Abstract: Understanding the relationship between large-scale structural and functional brain networks remains a crucial issue in modern neuroscience. At the large-scale, the structural (anatomical) network of hard-wired interconnections among mesoscopic brain regions is derived from diffusion tensor or diffusion spectrum imaging (DTI/DSI), while brain activity can be accessed, among other techniques, through functional magnetic resonance imaging (fMRI). Understanding this relation would have far-reaching implications myriad clinical domains, e.g. where and how to apply transcranial magnetic stimulation for stroke recovery. From a theoretical point of view, statistical physics has contributed to quantitative description of neural activities from brain anatomic structure though minimalist mesoscopic models. In this talk I first will present a stochastic model for brain activity at resting state, incorporating homeostatic plasticity mechanisms. I will show that –consistently with other studies, the optimal inferred model for brain activity is poised a critical state and that distance to criticality provide individual-based markers to evaluate the recovery of individual brain functional activity after stroke. I will finally raise some warning and caveats on recent results suggesting the controllability of structural brain networks as a fundamental mechanism to understand brain transitions between diverse cognitive states.