The linguistic abilities of LLMs are outstanding and continuously improving, so there is reason to ask whether the way in which they learn language is similar to how humans do; whether the generalizations they make match those of humans – and whether these generalizations align with the insights of theoretical, empirical and computational linguistics, for that matter. Due to the intransparent neural representations of LLMs, this is a difficult endeavor. All the more, such a research program could bring invaluable insights not only for computational linguistics and AI researchers, but also for theoretical and empirical linguistics. I will reflect on such research lines, take a brief look at recent work and insights that have been gained in this direction, and will extend these perspectives to neuroscientific research, which has a long tradition studying the ‘language network’ in the human brain. I will argue that integrating insights from all these areas could greatly impact future work in linguistics – be it theoretical, empirical, computational or neuroscientific. While most current research in this direction is devoted to syntax, I will showcase aspects of this emerging paradigm in our own work: studying the generalization abilities of LLMs in language-based reasoning tasks; investigating neural representations of Vision and Language Models, and how to integrate representations when combining language with Knowledge Graphs.