When you delete an Outlook item — email message, contact, task, appointment, and so on—Outlook moves the item to the Deleted Items folder.
Do you have this set up as an IMAP or POP account? If it is IMAP, all emails remain on the server (Gmail) and you will have to delete them there and check if there are settings you can choose (I don't have an IMAP account, so I don't know if/what the settings would be). If it is POP, you can set up when emails should get deleted by going to Preferences - Accounts - Advanced. However, some servers still keep emails for a certain amount of time and you will need to check the Gmail settings (in my case, Comcast's default setting is 30 days, but that can be changed). Barbara, while you are right that imap keeps mails on the server, you are wrong in saying you need to delete them on the server (well, of course you do, but not manually) the whole point of IMAP is that your local copy of mails (you download them like you do with POP!) will be synced with the mail server so both are the same and therefore all your mails are the same on all devices. So if you delete things in mail, they will also be deleted on the google server.
If you delete a message, it is moved to the trash, and it shouldn't show up in 'all messages' after that. If it still does, go to your mail preferences -> accounts -> select your account on the left -> mailbox behaviour.
Make sure 'move deleted messages to the trash mailbox' and 'store deleted messages on the server' is checked. After that, see if the trash shows up on the left side of mail under 'GMail -> Google Mail' if it does, select it, then select mailbox -> use this mailbox for -> trash from the menubar.
After that, everything should be working. Fwiw, I too have tried various incantations of preferences to try and get Apple Mail (on the desktop and iOS devices) to really delete gmail messages. I grew tired of messing with it and switched to gmail POP. (personally, I don't like the thought of all my email messages sitting on gmail's servers for very long to be searched/indexed/etc/etc anyway; but that's another topic entirely.) IMO, it's a combination of a non-standard mail server implementation (for both imap and pop) on Google's part, and Apple's inconsistent mailbox handling across their mail clients. How does minecraft for pc/mac [online game code] work?.
Maybe if Apple Mail on the desktop let you choose which folders (local or on server) are to be used for Drafts, Sent, Deleted like the iOS mail clients do, Apple Mail would be putting messages in folders on the gmail server where gmail actually expects them to be. Apple Mail's 'Move deleted messages to the Trash mailbox' and 'Store deleted messages on the server' are two of the most confusing and counter intuitive checkboxes in an Apple app. If the second checkbox actually said and meant, 'Store trash mailbox on the server' it would make sense. Some unix geek created those checkboxes back in NeXT days and they've stuck around ever since. Mac drive for windows free software. But I digress, sorry. The fact that Mac users have to struggle with Apple mail clients to work google's 'All Mail', 'Deleted Messages' vs 'Trash', etc is ridiculous.
Obviously, Steve Jobs has never had to fight with his mailboxes or these kinds of things wouldn't be a struggle for the rest of us. Ok, toyed with my gmail [imap] account across the Mac desktop and my iPhone and seem to have found a combination that actually works. (This is with Apple Mail from 10.6.4) *In Apple Mail on desktop:* - gmail IMAP account, Mailbox Behaviors pref panel: - uncheck 'Move deleted messages to Trash mailbox'. This will disable the second checkbox, 'Store deleted messages on server', which is what we want. - gmail account, Advanced pref panel - IMAP Path Prefix: '[Gmail]' (enter what's between the single quotes) *In Mail on iPhone:* - gmail IMAP account, Advanced settings: - Drafts Mailbox, set to 'Drafts' on the server. - Deleted Mailbox, set to 'Trash' on the server. - IMAP Path Prefix: '[Gmail]' (enter what's between the single quotes) Results: *With Apple Mail on desktop:* When you deleted something in Apple Mail on the desktop for the gmail account, it gets moved to the 'Trash' in gmail.