I have been using AT&T's messages.att.net for months. It worked well.
But then in January 2018 I got the following text message:
I called AT&T and they said to ignore it. That was wrong.
I started getting this response to https://messages.att.net:
After literally months of calls to AT&T their story was that they have discontinued this service except for non-phone devices, e.g. tablets and watches. Another story was that it only ever worked for AT&T branded phones. But we know different, don't we?
So I went off on a quest for alternatives.
I first tried Join. Here's a brief write-up on it.
I thought it was an interesting implementation. It uses your Google Drive as a place to store the text messages. It runs an app on the phone that watches the Google Messages app and sends the data to your Google Drive. Then I used Join's web version to view the text messages. In addition to the web presentation Join offers a Chrome extension and a Windows 10 app (paid).
The web version has a 60 second timer between updates and often paints the messages out of sequence and omits messages. The web version doesn't support displaying MMS pictures yet. The author said he will have to add that in the future. In a group thread you can't tell who the author of an individual message is.
The other presentation methods may address these issues but I wasn't impressed.
The next app I found was Pulse. Pulse is simple and fast. Here's a good write-up on it.
Pulse installs a replacement app on your phone for Google Messages. I wasn't wild about that but it really works nice. By being the default SMS app the Pulse app gets instant visibility of text messages. The Google Messages app still sees all the messages so apps like SMS Backup & Restore still work.
The web version requires you to create an account with Pulse and login to it. For that you get instant visibility to your phone's text messages. All of the issues I had with Join were solved with Pulse.
Both Join and Pulse are paid apps. Both also require that your phone is turned on and connected to data and cellular networks.
Post script: Just for giggles I tried messages.att.net again. It worked fine. My history was empty (it only goes back 90 days) but otherwise it worked.
Nah, not going back.
PS. Don't do anything until you read Part 2 next week.