iPhone not showing incoming calls but shows voicemail?

So I got a really weird problem with my iphone 5.

My iphone doesn't ring or show incoming calls but suddenly out pops a voicemail from the person. It's really annoying because I am currently job searching and I've missed calls from potential employers and have only known they've called because the voicemail which actually shows up no less then ten minutes after their call was made. This also has the added affect of me missing them as they've already left the office by the time I try to call back,

Now here is the wacky thing. It only does this on numbers not saved in my contacts. Like my Mom can call me and I see the number. Or my landlords. Or anyone I have as a contact I get their calls without any problem. Yet I don't see incoming calls from numbers not in my contacts list.

Any idea on how to fix this would be much appreciated.