It seems to me that there are three basic philosophical approaches to dungeoneering and the underworld in D&D. (They are specific to D&D and its mythos, such as it is.) They are:
- The Philotomical Approach, better encapsulated in the phrase "dungeon as mythic underworld". Here, the dungeon is a kind of antithetical reality to the surface world, ruled by demons or other powerful and supernatural entities, akin in a way to hell or Hades. Far from being just a set of tunnels underground, it is rather a kind of grotesque mirror to our own reality - the yin to our yang, the place from which true evil comes. This is the most supernatural or fantastical perspective.
- The Salvatorean Approach, which is (probably) the one which Gary Gygax took, best encapsulated in one single phrase: the Underdark. Here, the dungeon is a vast underworld, just like in the Philotomical Approach, and not just a set of tunnels underground, but here, it is still natural (in the sense of being naturalistic). It is knowable and works along comprehensible lines: there may be mind flayers, kuo-toa and drow down there, but at least those things are understandable as actual real physical entities. It isn't a well of infinite evil; rather, just a very bad place for surface dwellers while still being a living and breathing world in its own right.
- The Piecemeal Approach, in which there is no underworld as such - only separate dungeons. Over here is an ancient volcano riddled with caves and tunnels; over there is an abandoned castle; yonder is a ruined temple: all of them are dungeons, but none of them are anything more than that. They have bottoms. They are finite. This is probably the most 'realistic' approach.