How do mountain climbers retrieve ropes?

How do mountaineers get their ropes/anchors above them when they, themselves, haven't climbed that high (like when they're climbing steep, nearly 90 degrees, rocky mountains)? They're depicted as climbing on ropes, but

American Alpine Institute - Climbing Blog: Retrieving a Stuck Rope

Ok, is this a valid use of the hole on this ATC? Or just a really great way to get myself killed. I dont see why not but my gut is saying

How do mountain climbers retrieve ropes?

The 6 Best Rock Climbing Ropes

How do climbers retrieve ropes after a descent? - Quora

Bigfoot Mountain Guides: How To Use a Pull Cord For Rappelling

Rock-climbing equipment - Wikipedia

How I climbed a 3,000-foot vertical cliff -- without ropes, Alex Honnold