The last post addresses the narrative of a wholistic dungeon, in which the entire space is in play continuously ... and not just when the players open a particular door. Rather than a series of set pieces, in which various monsters and scenes sit waiting to be discovered by the players, these same monsters move towards the players aggressively, as soon as the players enter their space.
The more traditional form is passive, being laid out as a series of numbered rooms — we're all familiar with the format. In structure, the dungeon is a series of "if/then" statements. The players act and the dungeon reacts. This may produce a spontaneous interplay, such as a kobald running off the warn other kobalds, who then arrive to turn out the interlopers — but these events are rarely spontaneous. They're written into the dungeon's description ahead of time, so that "if" the players go here, "then" this happens.
For some years now, I've run my dungeons more loosely than this. In effect, I've ceased to make a distinction between the interior of a dungeon and the outdoor wilderness. In the wilderness, as the players travel, they either stumble into events or have events that stumble into them. A group of wolves spontaneously surround the player's camp, regardless of what the players have done. They crest a hill and see a large non-human encampment below, just a few hundred yards off. There's no intention on the player's part ... they're thrown into the situation and forced to grapple with it.
Whereas a dungeon is usually in the form that when the players want to stop, they just can. Each door and hall form a bubble that, if not popped, remains in perpetuity. This lets the dungeon function episodically, with each room having its own character, disconnected from other rooms. In the extreme, these rooms work like the Dungeon! game, created in 1975 by TSR and updated in later years.
There might be pockets of innocent monsters, stuck off in corners of the dungeon — non-intelligent monsters that rush forward to feed, or intelligent monsters who can provide exposition about the Big Bad. These latter may be too scared to help, or they might throw in with the party if they see that as an opportunity — and this too depends on what the party says, or what entreaties they make.
The flexibility of this format allows the introduction of new ideas from session to session, just as I might do with the wilderness if the players remained in a given valley over a long period of time. Because the dungeon isn't a carefully fitted-together jigsaw, the removal of some obstacle might reveal an altogether different part of the subterranean milieu that wasn't there or even conceived of last week. If the party finds cave-in, and takes time to dig through the rubble, they can expose a small hole that can be squeezed through ... and this unburies some other lair that's been divorced from the Big Bad and everything that's come before by perhaps 30 or more years. It's a part of the tunnels the Big Bad didn't know about, because it's only been here for, say, a decade.
By having the flexibility to add such "side quests" from session to session, I'm freed from the process of building a whole dungeon, top-to-bottom, before I can start running. I can start with a general idea — kobalds at the front door, a watery lair deep down, waves of amphibian and insect minions rushing the party as they descend — and then lay out the dungeon during the game itself, which I can do with a few minutes of graphic design on my computer. As the players can see my desktop as I design the room (I used to do this on a whiteboard), they have something to think about and talk about while I'm designing. Their attention is at a peak, wondering what the final image will be, and I'm not forced to draw rooms in the stale quiet of my room when players aren't there. This works for both me and the party, as it builds tension and invests both me and the players in the design process.
I recognise this is, for many, simply "wrong." For others, it seems impractical. It works for me because I've had so much practice drawing wiggly lines on a computer program that I can do it very quickly ... but in truth I've always disliked the pre-planned dungeon layout, mostly because I'm never sure it's all going to get used, as my parties, freed from the expectation of necessarily finishing a dungeon, often don't. Thus, I only need to make as many rooms as I'm actually going to use.