WiMax (IEEE 802.16) is a networking standard similar to WiFi. The former coming to phones is far off, primarily because it wasn't intended for mobile use. It is a very big network used to provide connectivity, mainly Internet in cities. It could be used for linking various WiFi hotspots and provide last mile conncetivity.
That said companies are working on the "mobile" version of it. Though how mobile is still a question, perhaps you'll find it integrated into lap tops, but I'm guessing for the time being that'll be it. Intel & Motorola are jointly working on something similar.
In India VSNL & BSNL have been testing WiMax for providing last mile connectivity in rural India. Also hearing something about Bharti having trial runs in B'lore and Delhi.
Digressing a bit on the mobile front, in future with the coming fo 4G you ought to get seemless connectivity independent of underlying technology. It's called Convergence.
The Indian mobile market is not mature enough to support technologies, first let 3G roll out, then let's wait for number portability. But before that what about Unified licensing??
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