Boost is cool, and boost code is generally complex. The Asio library is cool, complex, and not really well documented.
Boost.Asio docs from Boost. The best part is really the tons of examples, but examples always suffer from, well, being examples. There is a separate document also written by Christopher Kohlhoff that is also useful to read.
The author of Asio keeps a blog: http://blog.think-async.com/
StackOverflow thread Best documentation for Boost:asio points a few things out.
There is an online version of The Boost C++ Libraries by Schaling; chapter 7: Asynchronous Input and Output, is a decent read.
Oddly enough, while the Networking Library Proposal for TR2 was disparaged in the StackOverflow thread, it’s actually a pretty good thorough-yet-concise description of Boost.Asio. The down side is that it’s pretty old at this point (it was written in 2006). Maybe Boost.Asio has been really stable and hasn’t been changing a lot – I don’t know.
Introduction to the Boost C++ Libraries, Volume II – Advanced libraries has several chapters on Boost.Asio.
Interesting article on making Boost as a Framework for MacOS/iOS.