What's the difference between Barolo, Brunello and Barbaresco?

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Dear Dr. Vinny,
Can you please explain the difference between Barolo and Brunello wine styles? And how is Barolo different from Barbaresco, since they're both made from the same grapes?
—Elio M., Toronto, and Dominic F., Grand Island, N.Y.
Dear Elio and Dominic,
I remember, early in my wine-drinking experience, having a glass of Italian red that I loved but couldn't remember the name of ... except that it started with a "B." Barolo, Brunello and Barbaresco are all Italian wines, and they're all red.
Barolo and Barbaresco are both from the Piedmont region (the top left part of the "boot" of Italy), and both are made from the Nebbiolo grape, but they are named after the districts they hail from. Barolo and Barbaresco have wonderful, distinctive aromas of tar, roses, licorice and truffles. Barolo has a reputation for being more massively tannic and rich, while Barbarescos are more graceful and approachable, but there are many variations of styles out there. (There is one more Piedmont "B," and that's Barbera, which is the name of both the grape and the wine. Barberas are kind of the opposite of Barolos and Barbarescos; they're light and crisp, with lower tannins, and they drink well young.)
Brunello, on the other hand, is made from a particular strain of a different grape (Sangiovese) in a different part of Italy (Tuscany, near the center). The best versions of Brunello have luscious, bold, rich black and red fruit flavors. Decanting and aging is good for Brunello, when you give it a chance to express its complex aromas and velvety tannins.
—Dr. Vinny