These creatures, also known as coypu, look like a vague cousin of the beaver; they're a little smaller, have narrow tails and would look quite cute if it wasn't for their alarmingly orange teeth.
There's an established population in the Tiber River, and occasionally you'll see one swimming along the bank (unless you're trying to photograph them for a website, in which case they stay hidden).
Nutria originate in South America, but have been farmed around the world, both for their fur and for their meat. The meat is apparently extremely good for you, being low in cholesterol and high in protein, but perhaps suffers commercially by coming from an animal best described as being "a bit like a large rat, with bright orange teeth".
Either way, nutria (or coypu - the two words are interchangeable) farms seem to have been a bad investment, and their inmates eventually released (or escaped) into the wild, where they form their own little South American expat communities across almost all of mainland Europe.