iPhone hangs

Recently my iPhone hangs on a regular basis. It might have started with iOS 8, but I'm not sure exactly when. Some days it's better than others, but this morning I can't use it for more than about three minutes without the screen freezing. Sometimes it hangs for a couple minutes, and then all at once registers every time I touched the screen or buttons while it was frozen. Other times it hangs for a couple minutes, then reboots on its own.

But ultimately this is making my iPhone unusable for any practical purpose. 😟

Any ideas? One thing I tried was turning off background refresh, thinking that some app in the background was ha going not able to get some data. This does appear to have made any difference at all.