How rich functionality emerges from the brain from an invariant anatomical architecture remains a major mystery. Recent advances in brain imaging and applications of network theory to large-scale brain networks have started to dissolve this mystery. Structural connectivity of the brain is defined by the white matter fibres and functional connectivity is given by correlations of brain activations in grey matter regions. This talk explains how structural connectivity of the brain is measured by diffusion tensor imaging (DTI), functional connectivity by functional magnetic resonance imaging (fMRI), and how the brain connectivity is understood by application of network science. Recent network analyses of the brain suggest that modular and hierarchical structural networks are particularly suited for functional integration of local and functionally specialized neuronal operations that underlie cognition. Though structural networks constrain functional networks, task-related responses that require context-sensitive integration disclose a divergence between function and structure that appears mainly on long-range connections. I will present our recent works on panellation of the cortex into functionally specific regions from fMRI scans, which are based on spatially constrained spectral and subspace clustering. Using functional parcels of the cortex or regions of interests (ROI), we build functional networks that are then modularized to identify the functional modules of the brain. We will explain how the features extracted from structural brain networks from DTI scans are used to identify features that differentiate different stages of Alzheimer's disease (AD) and are able to predict cognitive measures such as memory and executive function.