This works properly only with IMAP.
WHAT IMAP GIVES YOU
Read a message on your phone and it shows as read on your laptop. File it into a folder and the folder appears everywhere. Sent items are on the server, so you can find what you sent from your desk while you are out.
SETTING IT UP
Configure each device with the same settings. Nothing special is required; IMAP is designed for this.
FOLDERS
Create folders on one device and they appear on the others. If a folder does not show, look for a Subscribe or Manage Folders option in that client.
SENT AND DRAFTS
Check each client is set to save Sent and Drafts to the server folders rather than locally. A client saving sent mail locally is why "my sent items are missing on my phone" happens.
STORAGE
Because everything stays on the server, IMAP uses your quota. Empty Trash and Junk, and archive very old mail to your computer if space becomes tight.
IF ONE DEVICE IS OUT OF STEP
Usually a sync setting or an old POP3 account left configured alongside. Remove the duplicate account.