At his small winery in the foothills west of Madrid, Fabio Bartolomei points out a few things the giants in the industry don't like to advertise: Their wines are made from grapes sprayed with pesticides and are tweaked with colorants, thickeners, and flavor enhancers. The founder of Vinos Ambiz takes the opposite approach, producing 8,000 to 12,000 bottles a year of tempranillo, albillo, garnacha, and a handful of other varieties with minimal intervention. Bartolomei and hundreds of other producers of so-called natural wines are now unnerving (or at least annoying) the big commercial players of the industry as restaurateurs, distributors, oenophiles, and an increasing number of ordinary drinkers seek authenticity in their wines.

The Establishment generally "views natural winemakers as weirdos," says Bartolomei, who lists what he does and doesn't do to his wines on the labels—though he doesn't have to. (Neither Europe nor the U.S. requires wine producers to list ingredients other than sulfites.) But the movement he belongs to, which began in France in the 1970s, has gained global momentum, with at least a dozen major expos held yearly from London to Tokyo. "Natural wine was considered hippie juice 15 years ago," says John Wurdeman, the American co-founder of Pheasant's Tears, a natural winery located in the former Soviet republic of Georgia that exports 70 percent of its annual output of about 60,000 bottles. The market is "growing at incredible speed," he says, with world-famous restaurants such as Noma in Copenhagen and El Celler de Can Roca in Girona, Spain, each stocking hundreds of labels. Jenny Lefcourt, co-founder of natural wine distributor Jenny & François in New York, says her company's sales have doubled since 2009: "It's not just Paris and New York anymore—we're selling across the U.S."

A January survey of 1,000 wine drinkers by market-research firm Nielsen showed 65 percent of 21- to 34-year-old respondents were interested in natural wine.