What are some of your solutions for helping your party visualize larger, complex dungeons? I have historically run games rather minimalisticly without maps and minis, relying on verbal descriptions. But when it comes to some of the more elaborate dungeons, like those presented in Princes of the Apocalypse, things can get confusing fairly quickly.

What are some solutions you like? What tips do you have for laying things out without slowing down the pace of the game? Drawing on a map every time a new room is entered seems slow-going, and like a single erasable mat might run out of space rather quickly. 

If you're doing theatre of the mind style play, just have some sketches of the complex stuff or change the elaborate pieces into something more your usual style and pace where possible. 

Or use the minis and things on the mat just to help keep complex stuff straight like distances or spaces. But just keep the minis out to be approximate the complex action.

You gotta do you.

Are you able to map out a small layout of a dungeon, without going into room detail?  Perhaps an overview on graph paper, displaying the room locations, dungeon pathing, etc?

I can understand not wanting the players to see the full layout, which would require covering up, but this would give you great reference points as you progressed through.  Keep notes on-hand or detail rooms on the fly as they're entered.

You will be impressed at how effective just a collection of casually drawn squares (rooms) joined with single lines (corridors) can be.

If you have been keeping track of simpler dungeons with descriptions alone, you don't need anything else: your players will keep track of what's in each box and have a feel of the layout, and it takes about five seconds to draw a square on a piece of paper.

You can very easily add a single note on each square (room), such as "kitchen" or "3 statues", and you instantly have a full reference that can remind people where they've been and what they haven't explored yet at a glance.

It is fun to let the players drawing things as the DM explains what it is in the area.

Using a bunch of colours is the key.

My first DM left the mapping up to us, he would describe the rooms and passage ways, and we would draw (we had grid paper and books from our maths lessons), the best part was that sometimes we stuffed up and that meant us getting lost, which was never a good thing when you are trying to flee a hoard of demon monkeys and you end up back in the room you were running from.

I always loved this way of DM describing and players mapping, however I don't get to do it because my group is all over the worlds, so maps are uploaded onto Roll20.

I like to hand a player some graph paper and let them map things out as I describe what everyone sees, but when a dungeon is really complex and the player trying to map things is likely to have to ask me to repeat details because it's unreasonable to expect them to keep up with everything - I print out a "player version" map that shows walls and doors, but has no labels and doesn't display anything that the characters wouldn't automatically see. Then the "mapping" player just has to make markings on that map to remind them what was found in each room.

It depends a lot on the group. If you have a group that is mostly visual learners than having printed/sketched maps or dry-erase grid tiles is a pretty easy to do. But if you have a group that doesn't need the visualization (for the most part) then have something that you can reference as the DM to give them an adequate description, and also to show them if they are having trouble with a particular aspect of the layout.

Personally, I am fine without visuals. The rest of my group on the other hand, not so much.