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With my iPhone 5 with iOS 7.0.2 on Wifi or on 3G my iMessages won't send (Progress bar stuck in the middle of the screen).
Rebooting or Airplane mode won't change anything.
There seems to be a bug with iOS7 :
To make it work again here is a procedure :
I had the same problem. I was typing in the subject line. Went to settings, messages and shut off the subject line! Works great now.