Iain McGilchrist:

"The Master and His Emissary" (Yale Univ Press, 2012)

(Copyright © 2011 Piero Scaruffi | Legal restrictions )
In general, i strongly caution against reading psychiatrists to find out how the brain works. They typically come from a highly theoretical background with little or no laboratory background and therefore limited notions of physical brain processes. This book is no exception. As a book on the brain hemispheres it belongs to the pop-psychology literature that became trendy after Pink's "A Whole New Mind" (2005). Science knows too little about the two hemispheres (or anything else in the brain) to justify the ambitious "i know better" statements that the reader finds in these books.
For what it's worth, McGilchrist thinks that the right hemisphere is the "master" that connects us to the perceived world whereas the left hemisphere is its "emissary" that analyzes those perceptions, breaks them down and turns them into abstractions ("detective" could have been a better definition). He thinks that this difference is peculiar to Western civilization, i.e. to brains of Western European and North American brains (i am just following his logic), but does not quite explain what is different about the Asian brain.
More interestingly, the book travels centuries of Western intellectual history and views it as a cosmic battle between those two tendencies. If you take cerebral lateralization as just a metaphor, then the book is interesting in its reinterpretation of Western philosophy; but even that is hardly revolutionary. I personally think that there were many more than just two forces battling to shape Western (and any other) civilization. Alas, we live in the age in which everybody is obsessed with dualism and has to find only two forces battling each other. And i would strongly recommend that the author studies the differences between, say, Indian and Chinese culture. Dumping them in the general "Eastern" category as Western intellectuals have often done is not only racist but just ridiculous. Indian culture is probably more similar to Italian culture than to Chinese culture, or, if you prefer, Italian culture is as distant from British culture as from Indian culture. And i am not sure where the Middle East would be in this racist-tinged cultural discussion.
One of the very first lines of his book reads: "Most scientists long ago abandoned the attempt to understand why nature has so carefully segregated the hemispheres". I don't know any topic that is more researched today by neuroscientists and evolutionary biologists except for consciousness and for the causes of the various neuro-diseases. Unfortunately, the scientists have come up with very few certainties.