This chapter analyzes instances of successful, partial, and failed unidirectional epistemic transfer between theoretical linguistics and neuroscience. I distinguish three types of transfer, depending on the nature of the linguistic knowledge involved: type-A knowledge, about language as such, essentially invariant across theories or formalisms; type-B knowledge, about alternative formal analyses of basic structures and operations in language; type-C knowledge, about the application of various computational methods to analyzing or modeling behavioral or neural data. I conclude that successful epistemic transfer may be achieved, under certain conditions, with type-A and type-C knowledge, and I present some examples of the strengths and limitations of each approach. Type-B transfer, however, in particular from theories of syntactic and semantic composition, so far has not led to new knowledge of the neural correlates and mechanisms of linguistic computation. I suggest that greater theoretical emphasis on algorithmic-level analyses, via a revised notion of linguistic competence and a new model of epistemic transfer, can bring formal linguistics and neuroscience closer together. Finally, I discuss the possible role of a computationalist psycholinguistics as a semi-autonomous 'bridge science', that could serve the aim of linking linguistics and neuroscience through algorithmic models of linguistic functions, aided by emerging methods and results in areas of computational linguistics, computer science, and AI.