Subcortical contributions to core linguistic computations (pertaining to syntax-semantics) remain drastically under-studied. We critique the cortico-centric focus which has largely accompanied research into these higher-order linguistic functions and suggest that, while much remains unknown, there is nevertheless a rich body of knowledge concerning the possible role of subcortex in language. We ultimately attempt to show that there is a clear place for subcortex in models of natural language syntax-semantics, including a role in binary set-formation, categorized object maintenance, lexico-semantic processing, morphosyntactic linearization, and cross-cortical representational integration. In particular, we consult models of language processing relying on oscillatory brain dynamics in order to investigate both the apparent and possible functional roles of subcortex in language.