What is the relation between language and cognition?

What is the relation between language and cognition? On the one hand, researchers like Noam Chomsky thought of language as an independent function with its own rules. However, other people – mainly psychologists – thought that language as a system is embedded in cognition and subject to all models of cognition. How do researchers currently view the relation between language and cognition? Have new techniques for brain research and research on cognitive functions led to a great change in this regard?

Here* you can find a recording of a recent debate that was held at the Cognitive Science Center Amsterdam with a panel consisting of Rens Bod, Annette de Groot, Jeannette Schaeffer, and Hedde Zeijlstra all working at the University of Amsterdam.

Interestingly, music showed up several times in the discussion as well.

* UvA streaming video; Sorry, only visible for UvA-students and employees.

Hauser MD, Chomsky N, & Fitch WT (2002). The faculty of language: what is it, who has it, and how did it evolve? Science (New York, N.Y.), 298 (5598), 1569-79 PMID: 12446899