Would you please give me a small introduction to wineglasses for red wines?

Hello there! I'm Dr. Vinifera, but you can call me Vinny. Ask me your toughest wine questions, from the fine points of etiquette to the science of winemaking. And don't worry, I'm no wine snob—you can also ask me those "dumb questions" you're too embarrased to ask your wine geek friends! I hope you find my answers educational, empowering and even amusing. And don't forget to check out my most asked questions and my full archives for all my Q&A classics.
Dear Dr. Vinny,
Would you please give me a small introduction to red wineglasses—in particular, the different shapes of them? I work as a waitress at a restaurant where we have a huge wine list, but we only have the common Cabernet glasses and the Burgundy/Pinot Noir-shaped ones. However, our guests often say they’ve got some huge glasses for their Shiraz/Syrah and other glasses for other wines, so they’re making me blush more and more with the question, “Are those the only types of red wineglasses you’ve got?” and demanding proper shapes for every grape. Would you be so kind as to tell me a little about the other types of red wineglasses, so I would know what to say to expressions of this growing demand?
—Radvilé, Denmark
Dear Radvilé,
In general, wineglasses for red wines are larger than wineglasses for white wines, but the stemware shapes are all designed to cater to each wine type, to best collect its aromas and allow it to "breathe," or benefit from exposure to oxygen, as needed. Among wineglasses for reds, you mentioned the two main categories: the Bordeaux-style glass, which is taller and has a relatively smaller bowl, and the Burgundy-style glass, which has a wider, shorter bowl.
Some wineglass makers get even more specific than that, designing glasses for specific varieties like Zinfandel and Syrah (both of which, by the way, are variations on the Bordeaux-style glass).
I find it unusual that diners would expect a restaurant to have something as specific as a glass for every variety. Sure, sometimes I’m at a restaurant and I wish they had better stemware. For me, that typically means thinner glass, or glasses with larger bowls so I can give my wines a healthy swirl. True story: I used to have a friend who would bring his own glassware whenever he brought his own wine into a neighborhood joint that was accommodating but casual. It was strange, but he had cleared it with the owner and he was a regular, so it was OK.
There’s a possibility your restaurant might want to invest in better-quality glassware, but there’s also a possibility that your diners are just very demanding. I think it can be OK for a diner to ask if you have different glassware, and you don’t have to blush about it, particularly for varieties that fall outside of the Bordeaux or Burgundy profile. You can say, “We typically serve Syrah in these Bordeaux-shaped glasses, but if you prefer, I can grab some of the Burgundy-style ones, which have a wider bowl.” You can always show them their options and let them pick. If I were a picky diner, I’d appreciate having a choice.
—Dr. Vinny