I have recently read reports of scam calls originating outside of the USA that target Mobile numbers, and they end up running-up very high bills on your account...

This caused me to look into call-blocking Apps for the iPhone, and a few popped-up in my search -- does anyone have relevant experience with Apps that do this, and can you share your feedback on which Apps work 'best'?

I don't. I've seen a few apps posted around 800 notes itself on different threads, but think to look into them.    I have a tracfone so don't even know if one of those would work on it..

I wish I could. I would've said Mr. Number, but my understanding is that it is now only available for Android. 

For future reference for Android users, though, Mr. Number is what I use, and it blocks unwanted calls and texts as identified by me. It's worked quite well, as the numbers I've identified as unwanted never even set off a ringtone.