I'm often asked if WiMax will replace Wi-Fi: In fact, I received such an email this morning. Here's the answer I sent in reply.
WiMax and 802.11n (and related standards) are somewhat unrelated. Wi-Fi is a local area network technology; WiMax (whether fixed, nomadic, or mobile) are wide-area network technologies.
Wi-Fi will continue to evolve as the best way to spread a network over an office or home or small area in which a cloud of service is needed. WiMax will probably evolve as a great replacement, alternative, or complement to fixed wired and mobile wireless services. That is, instead of an ADSL line or T-1 line, you might have a WiMax receiver on your roof or an antenna in your window. Instead of a cell phone that uses 3G to carry video or a cell data card for accessing a 3G network, you might have a WiMax-equipped laptop or phone.
Wi-Fi is a local distribution tool to push bits among users connected nearby; with many Wi-Fi base stations using the same name, you can build seamless coverage on a college campus, city park, or corporate campus. While it's being used for metro-scale deployment, that's because it's the best worst solution. It's not designed for that purpose, but everyone already has a Wi-Fi adapter, the technology works in unlicensed spectrum avoiding that issue, and it's highly commodified making parts cheap across the supply chain for consumers, vendors, and network builders.
Right now, you can get WiMax or WiMax-like fixed broadband pretty readily in most major U.S. cities and in a lot of urban and rural areas worldwide. It's very competitive in performance over shorter distances when you get to or over T1 or E1 speeds (roughly 1.5 Mbps each way). Several providers in the US already compete in some cities, and offer incentives like 24 to 48 hours from order to live access and free antennas and receivers with long-term contracts. Switching from a T1 to the equivalent of two T1s over fixed WiMax is often about the same price--sometimes a little less, sometimes a little more.
Mobile WiMax has a tougher row to hoe here in the U.S. as spectrum is scarce in the bands that are most likely for it to use: a few carriers own most of the desirable bandwidth. This means that even if it's financially viable and Intel rolls out WiMax adapters in laptops (as they plan to), you still have to find spectrum to offer service. A "mobile" WiMax base station can offer fixed, nomadic (a movable receiver that's static while in use), and mobile service.
Fixed WiMax has an easier time of it because it's primarily a point-to-multipoint, mostly line of sight service, and thus the sweet spot of lower frequencies needed for ubiquitous, seamless mobile coverage aren't as critical. There will be WiMax for unlicensed frequencies, and there's potentially some reserved spectrum in many countries and regions, including Europe, that could be put to use for mobile or fixed service.
That's the long answer. The short answer is that Wi-Fi and WiMax will continue down somewhat different paths because they serve different purposes. If WiMax ascends as a better means of faster, metropolitan access, Wi-Fi's importance in that role will dim. But WiMax isn't affordable or sensible as a campus-wide service yet, and it's unlikely to ever metamorphose into a Wi-Fi competitor.