The many different pieces of spectrum used for LTE is a problem that goes well beyond Apple, and travelers are not expected to be able to roam on these fast networks in foreign countries for several years.
The three models of iPhone 5 that are set to go on sale beginning Sept. 21 are specialized for certain markets.
One model, the GSM Model A1428, looks geared toward AT&T, the original carrier of the iPhone and a mainstay of Apple's U.S. phone business. It's built to use LTE in bands 4 and 17, both of which are deployed by AT&T. (T-Mobile USA's planned LTE network will also be in band 4, though that doesn't mean an AT&T iPhone 5 will work or even necessarily roam on T-Mobile, it only makes it possible to build units for that network.)
GSM Model A1429 seems suited for key Asian carriers: It has bands used by Japan's NTT DoCoMo (at 2.1GHz) and by South Korea's SK Telecom and LG UPlus (at 850MHz), along with the widely used 1.8GHz band.
There is just one model designed for CDMA, the type of 3G network used by Verizon Wireless and Sprint in the U.S. That phone, the CDMA Model 1429, includes the two Japanese and Korean LTE bands in addition to Band 13, used by Verizon, and Band 25, used by Sprint.
All three phones include support for four widely used bands for GSM plus four for its faster variants that go under the HSPA name. The CDMA unit includes three bands specifically for its variant of 3G, called EVDO.