Modern, non-invasive brain imaging techniques are providing unparalleled access into the living human brain, and the emergent complex data sets describing global architectures, of both structure and function, open up fasci- nating opportunities to characterise and understand what is perhaps nature’s most complex system. Recently, a number of studies have shown that brain injury and disease manifest via faulty, disrupted brain networks (e.g. schizophrenia, Alzheimer’s disease, multiple sclerosis and stroke). Yet, despite significant progress in our understanding of human brain connectivity over the past decade, clinical applications of network analysis of the brain are still in their infancy. In this talk, I shall provide an overview of the state-of-the-art in complex network applications to neuroscience, before considering a number of recent extensions in the area, the aim of which is to construct more physiologically realistic network models of the human brain via a combined theoretical/experimental approach.