Maybe your account is getting too close to filling and you want to search and delete messages smartly.
Note that if you delete them, they're not removed from your gmail space until you empty the trash.  So the sequence of actions could be:

1. Search for large emails, those from certain addresses, etc, and delete all of them.
2. Empty trash.

Examples

You want to have gmail put received email into a folder so you can collect similar messages together or delete them as a group at a later time, for example.

1. Decide how you want to identify incoming mail that should be forwarded to a specific folder.  You can search your inbox for something that matches, like: from:GoodStuff@spamforyou.com or from:*@macys.com but try searches till you find one or more that you want the search to find.
2. Create the folder.  Maybe, Adverts
3. In gmail, Settings (it's that gear in the upper right)
4. See all settings
5. Filters and Blocked Addresses
6. Create a new filter
7. (Here you put the searches, usually into From:.  If you have several, you can separate them with OR, as in: GoodStuff@spamforyou.com OR *@macys.com)
8. Create filter
9. Choose what to do when the message arrives.  Of note: "skip the inbox" (you'll see it in the folder), "Apply the label" Adverts, "Never send it to Spam".
10. Also choose "Also apply filter to N matching conversations".
11. Create filter

You can have many filters (I have maybe 100) and you can have many addresses in each filter (I have up to 40 or more in one filter).

I use this to stuff many emails that I might want to read but aren't essential, to a folder I call Adverts. Then when I run low on space, I can use search: In:Adverts Older_than:10d to select those in the folder older than 10 days, select them all, and Delete.

Suggestions from a thread on/about 20may2021. The wiki's author, Steve, is trying things out.  Here's his status;

• 23may2021 I am trying out Horcrux right now and will update this with my findings.
• I'll be trying Thunderbird next.

Depending on the size of the mailbox, you may be able to accomplish this all with just drag-n-drop, but there are some powerful apps for Mac OS that support this kind of task, for example:

FWIW, there are a lot of reasons one might want to do a bulk download/archive of an email account, the most basic being the security of having a local backup copy. Others may just want to escape Google. And for people with super large email accounts (> 2 million saved emails), it becomes increasingly important to shunt older email into secondary storage just to keep an email client from collapsing under the load.

–Glenn P. Parker

I successfully downloaded 15GB of gmail (everything through the end of 2020) with these instructions:
https://www.lifewire.com/how-to-export-your-emails-from-gmail-as-mbox-files-1171881
It went smoothly, and I can download more as I go along, and it should stay all in order. 

I also successfully tried out the mail client claws-mail, with which I can read and search my now-downloaded mbox files.
https://www.claws-mail.org
As far as I know you can also send mail using claws-mail, though that's not how I'm planning to use it. 

I created an account with a different mail provider.
Once I get myself all the way off of gmail, I can send and receive mail on that account and stay under the tiny quota by routinely (weekly?) downloading received mail into mbox files on my own computer, reading/searching these archives with claws-mail. 

–J Tang

I use https://takeout.google.com/ for all Google data downloads, including email. It's pretty straightforward and helps conserve my inbox space.

–Ethan Kiczek

I use Thunderbird on my Mac but it’s available for Linux and Windows. It may not be the most user-friendly? But I’ve been able to keep and save emails and move them from one account to another (dragging and dropping) without issue.
I should add that Thunderbird is free and it downloads my emails to my computer. So, for example, I have an old work email that I sometimes want to look at for reference and I can without any issue.

–Adam Schwartz

Your gmail account is using close to all of its space.  You want to make more room in your gmail account.  You can use the machine-based solutions above, but if you want all messages to remain online, you have some options.

1. Delete messages. 
   1. By size.  Search for "size:5m" and delete them, the ones that are over 5MB in size.
   2. Spam.  Delete your spam messages. (maybe: "in:spam older_than:7d" to access ones older than 7 days to delete 'em)
   3. Trash.  Empty your trash.
   4. By some other criteria. Maybe messages older than 1 year ("older_than:1y") and be sure to delete them from Trash to free up the space.
2. Buy more space from Google.
3. Or maybe there is another way.

Here is another way.  I've just found this today (20210812) and I'm still trying it out.  Here's what you do, and this list is preliminary and from memory, I'll update it after I do it again.

• Create a second gmail account.  Suppose your main account is "main@gmail.com" that is using up all its allowed space, and you create a second one called "second@gmail.com"
• Use Chrome browser.  This is the only one that has the needed extension.
• In Chrome, install the: "Multi Email Forward by cloudHQ" extension from the Chrome Web Store.
  • You will need to allow it to have full access to your gmail account.
  • There may be more setup needed.
• Once installed, go to your main gmail account.  Decide which message(s) to forward to your second account
  • Maybe set up a filter that puts all messages 5MB or larger into a folder called something meaningful like BIGGIES and these are the ones to move.
  • Setting up a folder holding the messages will make it easier to do the following steps.
• Go to the BIGGIES folder
• Select all messages (or a subset to try)
• Click on the Forwarding icon (it's between the Delete and the Mark-as-Read/Unread buttons, it's called Multi Email Forward.
• Forward selected emails individually …
• Dialog comes up, "Forward N email conversations to (enter email address)". This would be second@gmail.com
• Click away from where you enter the second email address, and "Forward Emails".
• Dialog comes up saying the messages have begun forwarding.

The transfer will happen in the background and it may take some time.

• The messages are forwarded; they show up in your Sent folder.  You should delete them there
  • You can identify them by date (when you did the forwarding) and by the TO address being second@gmail.com.
• The messages are not deleted from your main account.  You may want to delete these after you are comfortable with the messages being forwarded.

• The messages forwarded have a FROM of your main address
• The messages all show as Fwd:
• The date/time of the messages in the list of messages is the date/time you forwarded them, not the original send date/time.
• Each message is prepended with "Forwarded using cloudHQ's free email forwarding tool" with a link to the software

• You can forward messages from Main to Second, and safely delete them from Main, to free space there.  All while being able to access them on Second account.

• You get a Gmail Security Alert in your MAIN account every time you start the cloudHQ transfer.

Suppose

• You want the date/time to remain the same for message in Second as it was in Main
• You don't want the "cloudHQ" message in the forwarded messages
• You want more options

Then you need to purchase a subscription from the cloudHQ people.  As of this writing it's $14.99/month.  It would be nice if they offered different pricing for corporation use and personal use. But they don't appear to.

The following link tells how to effect a change to your email address.  Suppose you created your old email address using your birthday, and realize that this is not a good thing to do.  Read on.

From the link below, it says: There's no way to actually change the Gmail address linked to your Google account, but you can do so in essence by creating a new Gmail address and linking it to your original, established account. After creating the new Gmail account, change your settings so that messages sent to your new address will be automatically forwarded to your original account. You'll also need to change your settings so that you can send e-mail as your new alias from your old account.

After doing its steps, it would work as follows:

• Tell people to send to the new Gmail address. [it is forwarded to your old, birthday address]
• Use your old Gmail address to read and reply.  When replying, have Gmail use the new Gmail address as the sending address (you'd select it from a drop-down).

This is the link: https://www.wikihow.com/Change-Gmail-Address

This is collected from the previous 'Change Your Gmail Address' entry. You want to set things up so that messages you send can appear to come from another email address you have.

1. Sign into your gmail account
2. Settings, see all settings
3. Accounts and Import
4. Add another email address you own
5. In the "Add another email address you own" popup, type your other email address and check "Treat as an alias"
6. "Next Step", enter username and password for this other account
7. Click on "Add Account"

To use: Compose message and change the sender from the dropdown.

Notes for smi
Frustration.  [20220704] I have not gotten this to work yet.  I don't know what to put in for SMTP server, username, and password to gmail.