OK, this is happening to us. Two iPhones - SE and 6 - with T-Mobile simple choice plan. When we first entered Spain we got movistar LTE or 3G, and briefly Vodafone LTE, but getting closer to Barcelona we got movistar - no LTE, no 3G, nothing displayed after the name. Any attempt to use data tells us "can't connect to cellular network". We can call each other thank goodness. Texting sort of works - long delays sending with the iPhone SE and sometimes fails.

At least a list of providers eventually showed up when I took Carrier off Automatic. I'm going to try Vodafone ES or Orange SP, although right now in the hotel they say no service.

OK - I guess we going to have to try to understand the technical stuff above!

Oh, I should add that our phones worked great all over Netherlands and France - even during long car and train trips, and only getting close to Barcelona where this happened.

SOLUTION - in four steps, as guided by T-mobile support at the international number listed above.

At each point the support person checked to see if we had data.

1. Dial #766#

2. Go to Settings->General->Reset and select Reset Network Settings. Let the phone restart.

3. Go to Settings->Cellular and turn Cellular Data off for at least 5 seconds, then turn it back on.

4. Go to Settings->Cellular Data Options and turn Data Roaming on.

About a second after step 4 "LTE" appeared after the carrier name Movistar and we finally had cellular data!