How Can Homeowners Tell If Roof Damage Might Be Covered By Insurance?

I recently noticed some roof damage and I'm trying to figure out whether it's something homeowners insurance would actually cover. I've read that damage from storms is often covered, while wear and tear usually isn't, but it seems like there are a lot of gray areas.

If you've filed a roof insurance claim before, what was the damage, and how did you know it was worth submitting a claim? Did you have a roofer inspect it first, or did you contact your insurance company right away? I'd love to hear how it worked out for you.