Does an Underdark exist in D&D worlds other than the Forgotten Realms?

Question

Basic Rules, pg. 307:

Underdark Cities. The dark elves build fantastic cities in enormous caverns where food and water are abundant...

etc.

I realize we don't have settings books for Dragonlance, Greyhawk, etc. yet, but some published books do reference them (e.g. the Sword Coast Adventurer's Guide has a section titled "Class Options in Other Worlds"). On those other worlds do Drow reside in the Underdark? Does the Underdark even exist?

Since SCAG (and maybe other resources) seems to provide canonical answers for hypothetical questions such as "is Bladesinging appropriate to use with Qualinesti elves?" and since the Underdark is specifically mentioned in the Basic Rules I'm hoping there can be a canonical answer to this question. Material from past editions is fine if none exists for 5e, but consistency among those materials (i.e., no differentiation between editions) would then be important.

Answer 1

Greyhawk: Descent into the Depths of the Earth

The Underdark concept originated in Greyhawk with the in the AD&D adventure module Descent into the Depths of the Earth, published first as two different modules in 1978, and republished in a compilation module in 1981. See Korvin's answer for more details about this one.

Exandria

Matthew Mercer's world Exandria features an underdark, and is featured a few times in the Critical Role podcast. For canonical material, we see in Explorer's Guide to Wildemount that the Kryn Dynasty lived for a time in Wildemount's underdark before rebuilding their capital city:

Beneath the ruins of Ghor Dranas, a group of scavenging drow turned from Lolth, their primary deity for centuries, finding renewed faith in an esoteric entity they called the Luxon. Guided by the light of their new deity, the drow survived their ascent from deep within the Underdark and reclaimed the halls of Ghor Dranas for themselves, naming their new home Rosohna, or “Rebirth.”

And also:

Dark elves are the most populous race within the Kryn Dynasty. The drow were the first people to uncover the first buried Luxon beacon many ages ago, in a time before they turned from Lolth and escaped enslavement from the Betrayer Gods. The dark elves claimed the dread citadel of Ghor Dranas as their own, as well as the massive network of underground caverns that make up the Underdark of Wildemount. The Kryn are stealthily becoming a force to be reckoned with.

Eberron

Eberron calls their underdark "Khyber", and it is featured in a section of Eberron: Rising from the Last War:

Any time someone descends below the surface of the world, they enter Khyber. But the underworld takes two very different forms. First is the natural realm, networks of tunnels and caverns formed from stone and soil. These passages are dark and dangerous, but they’re exactly what you expect to find in an underground realm. Such passages might be home to carrion crawlers, giant beetles, or clans of kobolds. But ultimately these mundane caverns follow the laws of nature.

There’s another aspect to Khyber: go deep enough and you find a seemingly endless array of demiplanes, each stranger than the last. When descending into a chasm, you could find a labyrinth inhabited by demons or discover a realm consisting of the guts of a colossal living creature. Anything is possible in Khyber, and these “worlds within” are home to all manner of terrors.

Answer 2

The Underdark originated in Greyhawk, not the Forgotten Realms

The modules D1 and D2 which followed the original three Giants modules, came out in 1978 and were the introduction of the Underdark via module (and given that the author was E. Gary Gygax, it was set in Greyhawk). It's where the drow originate (in terms of game play; the first ever encounter players had with this monster/NPC) and live/lived. Drow live in the underdark; it had become their homeland (where they crafted their unusual armor that degraded in sunlight). Further lore/exposition on the drow homeland was in AD&D1e Module D3: Vault of the Drow, also introduced at GenCon XI)

The Wikipedia article for Descent into the Depths of the Earth summarizes the plot as follows (I am not where I can get at my original modules):

The plot of the original modules Descent Into the Depths of the Earth and Shrine of the Kuo-Toa places a party of player characters (PCs) on the trail of the drow priestess Eclavdra through the Underdark, a vast subterranean network of interconnected caverns and tunnels, battling various creatures on their journey.

Those adventures were very, very popular. As a result, the Underdark as well as the existence of Drow, deep gnomes, kuo Toa, et al, was subsequently ported (or adapted) into other setting like the Forgotten Realms, Eberron, and more recently Exandria.

Answer 3

Yes, other worlds often have subterranean regions, and drow often live in them. They are even, often, called the Underdark. For instance, the world of Oerth, for the Greyhawk setting, had its own Underdark (though also called Underoerth or Deep Oerth).

Other worlds can do different things, though—Eberron’s subterranean region is called Khyber, and drow don’t live there, they live on the surface, on the jungle continent of Xen’drik.