It's hard to make a good non-alcoholic beer, as anyone who's tasted one recently can probably attest. These beers start off their lives as regular, fully-alcoholic brews. After fermentation and before bottling, the beer is cooked at a low temperature, sometimes under vacuum. Since alcohol has a lower boiling point than water, it evaporates quickly and leaves behind the newly non-alcoholic beer.
Cooking does change some of the flavor and aroma compounds in the beer, much like pasteurization does for milk and other beverages. The most delicate flavors and aromas, particularly of hops, are lost during processing. This creates beers that tend to be malty, lightly flavored, and without much nuance of flavor.
Not all the alcohol is ever fully evaporated. That 0.5% limit from the Prohibition is still the legal limit for beverages marketed as non-alcoholic. This is generally not enough to make you intoxicated, but is good to know if your aim is avoiding alcohol altogether rather than just avoiding getting tipsy.
What do you think of non-alcoholic beers?