Communication between embdedded system and Mobile phone
If your bandwidth requirements are less than ~230.4 kBaud or so, then the cheapest and easiest way is to use one of the many HC-05 (or similar) serial BT modules available from eBay.
(EDIT - note comment from Chris on iPhones below)
Here's an example (you can also get versions with a pin header for through hole or breadboard use):



They may claim faster speeds, but in my experience with a few of them, the best performance I have had without issue is 230.4 kBaud (of course this may also be due to the paired modules capabilities also, though my module stopped responding to AT commands when set to higher speeds)
 If you need better performance (and datasheets) there are also better quality (and more expensive) modules available from the major vendors such as Farnell, Mouser, etc.