Perhaps this is something new to the 5s that I am just now running into. I didn't check why I had no new voicemails until I got a call from someone that always leaves a voicemail. On my iPhone 4 and on every other iPhone I've encountered up to and including a 5c, the voicemail tab was the same and the phone owner was notified when a new voicemail was available. I discovered that my voice mailbox was full, so don't know if this is an artifact of that or something new. Now, I have a button to call voicemail and have to login and deal with the voicemail system as if dialing in from another phone. I can't keep mails on my phone, get no notifications of new messages, nothing. Is there a way to go back to getting notified in the notification center when I get a new voicemail, being able to listen to and relisten to voicemails actually on my phone and all of that? I really, really dislike having to hit the call button, login and deal with the tedious external voicemail system and hope that this is not the only way to do things now. It makes me feel like I've jumped back over a decade to my old Virgin Mobile flip phone, except even clumsier.
Any info would be greatly appreciated. I've looked around in settings, but am not finding any place under phone or general to change the settings. Perhaps I've just missed it, I hope.