Neurological and neuropsychiatric disorders are major causes of morbidity worldwide. A systems level analysis including functional and structural neuroimaging is particularly useful when the pathology leads to disorders of higher order cognitive functions in human patients. However, an analysis that is restricted to regional effects is impoverished and insensitive, compared to the analysis of distributed brain networks. We discuss the issues to consider when choosing an appropriate connectivity method, and compare the results from several different methods that are relevant to fMRI and PET data. These include psychophysiological interactions in general linear models, structural equation modeling, dynamic causal modeling and independent components analysis. The advantages of connectivity analysis are illustrated with a range of structural and neurodegenerative brain disorders. We illustrate the sensitivity of these methods to the presence or severity of disease and/or treatment, even where analyses of voxel-wise activations are insensitive. However, functional and structural connectivity methods should be seen as complementary to, not a substitute for, other imaging and behavioral approaches. The functional relevance of changes in connectivity, to motor or cognitive performance, are considered alongside the complex relationship between structural and functional changes with neuropathology. Finally some of the problems associated with connectivity analysis are discussed. We suggest that the analysis of brain connectivity is an essential complement to the analysis of regionally specific dysfunction, in order to understand neurological and neuropsychiatric disease, and to evaluate the mechanisms of effective therapies.