“I know that I know nothing”

Not all the sparkling wine you drink has been refermented by the producer (both for traditional and tank method)
Many producers do not have the material means (the tanks or the space) or the know-how to carry the refermentation process on their own premises. Thus, in many cases the wine is loaded in tanks, put on trucks and sent to a contract company which will do the job for them.
Talking about Italy, it must be noticed that each denomination of origin has specific rules about where the production must take place, refermentation included. However, if you are making it outside the denomination system you can sent your wine everywhere in the Country.

Italian “Vino da Tavola” cannot be varietally labelled, but there are exceptions.
I already knew that still “Vino da Tavola”, the lowest level of Italian classification system, can be varietally labelled only when the grape is one of the following: Cabernet, Cabernet Franc, Cabernet Sauvignon, Chardonnay, Merlot, Sauvignon and Syrah. What I didn’t know is that this rule does not apply to sparkling wines: in this case any variety registered in the National Registry can be indicated (with exceptions).
You may find these wines qualified as VSQ, meaning Vino Spumante di Qualità (Quality Sparkling wine, when pressure >= 3.5 bar) or VS, Vino Spumante (Sparkling wine, pressure >= 3 bar). When aromatic grapes are used the two acronyms will become VSQA and VSA.

Barrel fermented red wine
Barrel fermentation is generally associated with white wine production because red wine is fermented with the grape skins and separating these from the juice may be too much of an hassle when it has to be done in wood.
However there are exceptions: for example Gloria from Ostatu winery (Rioja Alavesa) is fermented in open top small barrels. When I asked to producer Gonzalo Sáenz de Samaniego how they manage the skins thereafter, he replied that they simply take the barrel and pour the content in the press. The free run juice will flow down and the skins will remain behind, ready to be squeezed.

Punching down, literally
Gonzalo also explained me how they punch down the grapes for Gloria. They do not use hydraulic pistons or paddles, they do that by hand! His brother will stand in front of the barrel (225 L) and push the cap down and down again, enhancing extraction of color and tannins. They like to do a relatively short maceration (around 15 days) at a relatively low temperature (for a red of this stature), but with frequent punching down. The video is on Facebook and I cannot embed it, but here is the link.
“Isn’t it dangerous with all the CO2?” “No, the barrels are small, there is no problem.” he answered. Anyway it is the first time I hear of such a process.