I looked into this a couple of years ago, but didn't get anything as my lawns are too small to justify the cost. But I was impressed with the tech.
You just need to peg or lightly bury a control wire around the perimeter (or pay someone a few quid to do it for you) and then the mower trundles around clipping all the grass all the time (and dropping the clippings - maybe some have a bin, but I've not seen that). The wire stops them escaping (somehow), and they just change direction if they bump into something. You can go with GPS, but it doesn't seem worth the extra cost to me.
You also need the base station with power to recharge the batteries - the mower RTB when it needs some juice. A solar-powered base station might be an option in a sunny country.
Some mowers only work on smooth level lawns, but there are some that can handle rough terrain and surprisingly steep slopes. Husqvarna does a fabulous articulated AWD thing for about £5,000, but you should be able to get something fairly heavy-duty for £800-2,500.
The top-of the range ones have App connectivity, so you can see on your phone where it is and what it is up to, which would be cool if you wanted to be able to remotely monitor it in Italy from somewhere else. They also have anti-theft tech, like Ukrainian tractors.