This is an excellent book that adds much to the debate on the evolution of language. Similar to other scholars who espouse a usage-based, construction grammar approach to language and cognition, Christiansen presents arguments in favor of language being the adapted to the brain, rather than vice versa. Under this view, language acquisition, processing, and evolution can/should be studied in tandem (i.e., Culicover's argument).
The discussion and development of the Chunk-and-Pass strategy (Chapter 4) also makes a strong case for a parallel architecture of grammar (Jackendoff 1997, 2002). The notion of chunking has also been treated recently in generative approaches (Fasanella & Fortuny 2016), and represents a possible fertile ground of research on language and cognition from myriad perspectives in the future.
My only 'criticism' of this work is the short shrift Christiansen gives to alternative generative and emergent approaches to modeling grammar, which, at least at first blush, appear to also be ideal candidates for Chunk-and-Pass processing (such as LFG, HPSG, and the family of Harmony Theory grammars).