Some open theoretical questions are addressed on how the mind and brain represent and process concepts, particularly as they are instantiated in particular human languages. Recordings of neuroimaging data should provide a suitable empirical basis for investigating this topic, but the complexity and variety of language demands appropriate data-driven approaches. In this review we argue for a particular suite of methodologies, based on multivariate classification techniques which have proven to be powerful tools for distinguishing neural and cognitive states in fMRI. A combination of larger scale neuroimaging studies are introduced with different monolingual and bilingual populations, and hybrid computational analyses that use encoded implementations of existing theories of conceptual organisation to probe those data. We develop a suite of methodologies that holds the promise of being able to holistically elicit, record and model neural processing during language comprehension and production.