There are several serious gaps dividing theoretical linguistics from the rest of the cognitive science and engineering of language. I will attempt to identify several of these gaps and discuss work aimed at overcoming them. The work is guided by the conviction that theoretical linguistics can constructively engage with both experimental and computational research, addressing linguistic performance as well as competence. Contributions go both from and to linguistic theory. The research I will discuss (which focuses on phonology) provides an introduction to the recently published volumes, 'The Harmonic Mind: From Neural Computation to Optimality-Theoretic Grammar', written jointly with Géraldine Legendre (MIT Press, 2006). A number of the connections developed in this work are enabled or enhanced by an Optimality Theoretic conception of grammatical theory.