Noninvasive neuroimaging methods are invaluable tools for exploring the neural basis of the human mind. My focus is on language function as an integral part of human cognition. At the same time, language offers a valuable cognitive probe for assessing the type of information that can be extracted with brain imaging. Descriptive language models, largely based on observations of patients with language disorders, serve as a useful conceptual framework. However, computationally explicit models of language are needed to link behaviour to neuroimaging measures for an in-depth understanding of the human mind and language function. Such models may now be within reach owing to the accumulating imaging data, increasing understanding of the functional significance of the different measures, and adoption of machine learning approaches used in the field of language technology. Besides the obvious relevance to language and imaging neuroscience, well-defined behavioural-neuroimaging models will feed back to language technology for improved practical solutions, as well as lay the foundation for a rigorous, individual-level assessment and potential rehabilitation of language disorders. This type of work is necessarily multidisciplinary: experimental and methodological expertise must live side by side and be constantly exchanged in common research projects to educate a new generation of individuals with genuine interdisciplinary knowhow supplementing strong primary fields of expertise.