We call them hornets, but they are actually a species of yellowjacket, but twice the size of other yellowjackets and sporting white rather than yellow. Like their cousins, a single queen hibernates through the winter underground or in a crevice somewhere. The young hornet queen emerges in the spring and starts making the paper nest and rearing a first generation of sterile workers. These take over building the nest, foraging, feeding the next generations of larvae, protecting the colony, and so on.
The big, papery globes are a dramatic structure to find in the woods - especially compared to other yellowjacket hives, which never appear as anything but a hole in the ground. I had assumed the smaller cousins just dug burrows like ants, until a few years ago I had a colony that chose to live under a log right by the front door. One night I took a can of bug spray, (left by the house's previous owners) intending to tip over the log and spray insecticide down the hole. But when I turned the log, it came up with a torn, volleyball-sized paper nest. I was glad I'd approached it at night when the wasps weren't prepared, or the ensuing massacre could have gone the other way.
But generally, unless they build somewhere especially inconvenient I leave the wasps alone. It's true that they make off with the compost meant for the garden (together with the jays, raccoons and deer), but they otherwise don't bother us. If they take the occasional caterpillar from the garden, so much the better. And besides, I think our unpainted outdoor furniture has never become splintery because we have the hornets and other paper wasps who come and strip off the outer layers of wood all summer long.