Nowadays, cheese fondue tends to refer to one specific dish: melted cheese (sometimes mixed with corn starch or flour) flavored with garlic, and white wine or brandy, served in a communal pot over the heater.
But there was a time when the term wasn’t so clear: over the years, cheese fondue has been simply melted cheese with wine (served with bread to dip), melted cheese mixed with milk and eggs (something akin to fluffy scrambled eggs), and finally settled on what it is today in mid-to-late 1800s, in the Alpine region.
Swiss-style fondue is traditionally made with Gruyere cheese, sometimes by itself, but often mixed with some other type of Swiss-style cheese like Emmental, Appenzeller, Sbrinz, or Vacherin.
French-style fondue tends to use Comté cheese (both young and mature) as the basis and, similar to Swiss-style, often adds some other cheese as well. Soft french cheese like Reblochon, Camembert, and Brie are common choices for their melting abilities.
Italian-style fondue is the most unique, as it tends to mix cheese with milk and egg yolks for a richer and creamier texture. The cheese most often used for Italian-style fondue is Fontina.