AT&T settings issue - fixed very quickly
I couldn't send or receive texts from my iPhone. I took it to an Apple store, who spent over 1/2 with it and determined it was an AT&T problem.
I then called AT&T's customer support and spoke to an iPhone specialist, who transferred me to someone else at AT&T. That person told me it was because AT&T's text settings for my phone were not correct. Fortunately, it took her only a minute or two to fix it and now it works just fine. Total time on the phone with AT&T (including wait time) was less than 15 minutes!