Just wanting to see what other people do to record their campaigns.

I (somehow) became our groups historian, and am doing it on a google drive doc just so someone else can add to it if I'm not there (and my hand writing leaves something to be desired). Do other groups have a "historian" or does it all get noted down by the DM?

I started off just writing the notes for my character, but it ended up starting to take notes for the whole group. It's a bit haphazard, I just note the big stuff, I assume that if any of the characters are given clues along the way (and my character isn't there), that player will note the information.

Next campaign, I'm planning on going back to a hand written history, so it can be a bit more organic (can take notes easier in a book (also make it a bit easier to sketch out maps if needed.

Generally a lot of our character stuff is kept on the DDB player sheets online.

In my group, I assign different tasks to our different players in order to help ease the burden of my in-game responsibilities as the DM.

I have a group historian who is in charge of writing down histories, and uses a google document in the same way it sounds like you're using it.

There are other online tools such as World Anvil and Obsidian Portal for wikis and article entries. There's also lots of notebook style apps that are for general and specifically for D&D uses that can be very optimized for your game recording.

Before I moved, I was using Arcana Note as a DM's journal, and that was pretty great. There are a lot of fun Player's Notebooks out there, but honestly, a plain ol' notebook works just as well.

My character keeps an in game journal, which I actually write down in a little journal, and then I also volunteered to write summaries of our game sessions, which I type out as they are often pretty long, so it's a bit of both for me.

Having set up fairly recently, we have a campaign diary text channel on the discord server we used. 
This is essentially the notes section that will help players track time, and recall encounters/names
However, we haven't really progressed this to a coherent story yet - but if any of the players are interested in writing it - at least there's a section of chronology and reminders to enable it. 

I do like the idea of a team "scribe" that provides summaries (if you can find someone willing - as the DM of a campaign, I'd prefer to see this coming form the player side as it would offer a personal angle and aspect on the story. as the DM you will always be slightly "tarnished" by knowing what lies ahead) 

I am self-appointed historian for our group, and I literally just have a word document open and type out a shorthand narrative of the story. Then I go back later and flesh it out into a full story.