Research on multilingualism and the acquisition of language(s) faces numerous challenges given its inherently interdisciplinary character. This discussion will focus on the notion of internal context, a concept that forcefully demonstrates the need for integrating linguistically-oriented research with cognitive research in general. Investigating the internal context of language processing centres on the 'interpreted' world inside individual minds together with all the cognitive mechanisms that shape it. It will be argued that explanations are required that must go well beyond accounts of the linguistic properties of individuals' grammatical abilities and that, for this purpose, theoretical broad-based frameworks are needed that can act as 'base camps' facilitating explorations that venture beyond purely local domains and allowing findings from different research areas to be integrated within a shared perspective of how the mind works.