These thicker bottles are perfect for bottling brett beers, that tend to overcarbonate, as well as other highly carbonated styles, such as hefeweizen and non-sour Belgian styles. I like to bottle my sours in champagne bottles, even though they are stable beers, because it adds a little fanfare opening a corked bottle. Reusing these bottles can be as easy as adjusting your bottle capper to accept larger caps (if you own the red wing capper or a colona capper) or using a hammer to gently tap in cheap plastic corks and tie them down with wire harnesses. Since you pay a premium to buy beer in large format, you might as well reuse the bottles and get some value back out of it.
Most people are familiar with the 750ml wine and champagne bottles but you may not be aware of the larger bottles. Champagne/wine bottles go as large as forty liters! Sometimes you find 1.5 and 3 liter bottles of champagne but it's extremely rare to find anything larger in a store. I don't think I've ever seen a non-carbonated wine in anything larger than a 750ml but they can be found. Yesterday I bought a 1.5 liter bottle of champagne at Costco for $17 that will get opened on Christmas and then it is going to become a party bottle that I'll refill with homebrew to take to parties.
Occasionally you can find commercial beer packaged in 1.5 and 3 liter bottles. Chimay puts Gran Reserve in three liter bottles (I am sitting on a bottle from a 2010 bottling) and Duvel also does three liter bottles and I believe 1.5 liter bottles. Anchor puts its holiday beer in 1.5 liter bottles. St. Feuillien puts its blond in bottles ranging from 1.5 liter up to nine liters. A few other breweries also bottle the occasional 1.5 and 3 liter offering. It's far more expensive to buy beer in these larger formats, so the only reason it makes sense is to open it on a special occasion where that big ass bottle is going to be the centerpiece of the event (which is why I bought mine).
Each wine/champagne bottle size has a specific name. Below is a chart that I screen chopped out from this website that shows the most common sizes. I don't have any idea who decided these names were appropriate but now you know what to call big ass bottles.
But this wikipedia page has a more extensive list and offers some alternative names for the bottle sizes below Magnum. As far as beer goes, I have only seen half-bottles, bottles, magnums, jeroboam, methuselah and salmanazar bottles. I don't think I've actually seen any type of wine in anything bigger than a jeroboam (sometimes called a double magnum). The only half bottles I've seen with beer are the Lindemans, Timmermans and Chapeau lambics. I've only seen quarter bottles in four packs of Asti and I'm pretty sure the openings on those bottles are smaller than 12oz bottles, so I'm not sure how a homebrewer could reseal those.
As I said above, it's pricey to buy beer in those larger formats but if you can come across those larger bottles already emptied then it's worth nabbing them for refills. Sometimes you can find champagne magnums and jeroboams emptied out at NYE parties. I'm not a believer that beer ages any better in larger bottles, the only real reason it makes sense to pick up larger format bottles is for the wow factor of showing up at a party with a big ass bottle.