Snapdragon processors are popular but they are not the only processor supported. Most processors are qualcomm like the processor used in the Lumia 900 which is a Qualcomm APQ8055 + MDM9200 (WCDMA) but Samsung uses an 1.4 GHz Scorpion processor in the Focus S
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Qualcomm makes a SoC. It's called:
Snapdragon. Snapdragon includes a CPU, GPU, camera ISP, memory controller, and normally, a celluar radio (GPRS, EDGE, CDMA, etc) in a single IC (in addition to a lot of other components).
The CPU architecture is called "Scropion." It is ARMv7 ISA compatible (Cortex A8/9/15 are, too). It's performance, per clock, is slightly higher than a Cortex A8 design.
The GPU architecture is called "Adreno," designed by a former part of AMD (specifically, a former part of ATi, pre-AMD aquisition) that Qualcomm bought for pennies back in the '08/09 time period.
All WP7 devices, so far, are mandated to use one of several Qualcomm 1st and 2nd (Qualcomm calls them "S1" and "S2") generation SoC (System-on-Chip) models.
WP7 leverages the limited power of this old workhorse very well, as a result, its GUIs response is much smoother than most, if not all, competing platforms.
Don't worry about effective performance - all WP7 devices have more than enough to ensure the user will never feel the system is "too slow."
Currently, the S1 and S2 Snapdragon by Qualcomm chips are the only chips allowed, since MS WP7 is close to metal. Android is run on a VM layer, so it supports many SoC, at the cost of raw performance. iOS (Apple) is also close to metal, and only has, generally, 1-2 SoC designs supported by the latest OS (on an ISA level, the last 3 iPhones are nearly identical).
The last part was a slight edit/branch out to respond to the post that appeared above mine.