The dry stone huts with conical roofs are a Puglian tradition, dating to around the 17th century or so.  Originally constructed as agricultural storage, they dot the rural landscape of the area. 
A couple of hours north of our rental villa was the commune of Alberobello, chockablock with residential Trullis. Driving around the hills en route would reveal a Trulli house with many conical rooftops, or “Hobbit Houses,” as the children called them. 

The heart of the Trulli district is a declared UNESCO site, which roughly translates to lots of tourists and tchotchke-shops. We arrived in the late afternoon, thankfully, after the buses had started transporting tourists back to Bari and other cities and could enjoy our walk through the district.

 Within the main district the Trullis are mainly shops and stores, though there are a few residential homes.

 Some of the Trullis are decorated with Christian, Pagan, and Magic symbols.

In a neighboring commune it is possible to rent Trullis as holiday homes, which we did for an overnight on our return to Vienna. Completely modern and way fun, even if the shower ceiling was perhaps a tad low for the taller Hobbits in the family.