StuporDave is correct as to how they arrived in N.A. . The Nutria will destroy swamplands (like swamplands could be any less desirable) by eating not only the grass shoots but the roots as well. They were imported for the fur trade then released into the wilds when there was no more profit from them.
I'm told that the state of MD had placed bounties on them at one time and that there were quite a few people who visited the killing grounds, they breed like rabbits. There is no bounty on them anymore that I know of.
Some friends and I had the opportunity to go down to the Blackwater Swamp near Venice, MD. There were four of us and we took the boat and just steered down canals winding through the swamp. We all used .22lr rifles, 10/22's, Marlin M60 and a pump .22lr, when we would see one swimming down the canal we would cut the engine and coast as close as we could then all four of us would open up on it. It was a blast, we never hit them half the time, everybody competing to be the first one to hit it, water flying all over.
We were amazed after examining the first kill, them things are butt ugly, just as in the photos. After awhile we got out on foot and spread out walking as far as we could and popping them along the way, some would run like crazy and others would just stop and pretend you didn't see them, those weren't much sport, but notches anyway.
Almost as fun as the prairy dogs in MT