Why can't I see incoming sms messages?

[AC Question]

cannot see incoming sms messages

I know an sms message has arrived because my Samsung Galaxy S4 mini vibrates. I swipe the screen to unlock it and a message appears briefly at the very top of the screen telling me how many unopened messages I have. The messages do not appear anywhere in the Messages app, eg the conversation window.
I have switched off & on, checked the date is correct, reset all kinds of what seem like random parameters - all to no avail.
I am new to the Android OS. what can I do to see these messages/receive them correctly?

 

[N4Newbie]

If you have an app called Hangouts, open it and see if they are in there.