One longstanding impediment to progress in understanding the neural basis of language is the development of model systems that retain language-relevant cognitive behaviors yet permit invasive cellular neuroscience methods. Recent experiments in songbirds suggest that this group may be developed into a powerful animal model, particularly for components of grammatical processing. It remains unknown, however, what a neuroscience of language perception may look like when instantiated at the cellular or network level. Here we deconstruct language perception into a minimal set of cognitive processes necessary to support grammatical processing. We then review the current state of our understanding about the neural mechanisms of these requisite cognitive processes in songbirds. We note where current knowledge is lacking, and suggest how these mechanisms may ultimately combine to support an emergent mechanism capable of processing grammatical structures of differing complexity.