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Syntactic complexity has always been a matter of intense investigation in formal linguistics. Since complex syntax is clearly evidenced by sentential embedding and since embedding of one clause/phrase in another is taken to signal recursivity of the grammar, the capacity of computing syntactic complexity is of central interest to the recent hypothesis that syntactic recursion is the defining property of natural language. In the light of more recent claims according to which complex syntax is not a universal property of all living languages, the issue of how to detect and define syntactic complexity has been revived with a combination of classical and new arguments. This volume contains contributions about the formal complexity of natural language, about specific issues of clausal embedding, and about syntactic complexity in terms of grammar-external interfaces in the domain of language acquisition.