I used to use Gnus, which is really bad for blocking (I used to run it in a separate Emacs instance).

Mu4e is pretty good in this respect: it offloads most of the mailbox processing work to the `mu` command, which it runs asynchronously. I fetch my email with a system service, external to Emacs.

I have a bunch of IMAP and exchange accounts. Any chance I can use them in Emacs? Last time I checked only POP3 was supported.

I am a mail account hoarder (9 so far and more coming) and offlineimap together with mu4e is the best email client for multiple IMAP accounts across multiple mail servers. For sending mail I have message-mode and smtpmail.el (both come with Emacs) set up to handle composing and replying across the multiple email addresses. I also set up smtpmail to queue mail and run in a sub-process - this gives gmail-like "undo sending this email" functionality, ability to compose and reply to messages off line, and most importantly does not block the parent Emacs process when sending email, while providing better error and progress output.

Planning to write a blog post about this configuration, but in the meantime I am happy to share privately - [email protected]

Gnus does do IMAP. Receiving from multiple accounts is easy, though sending from multiple accounts take a bit of work. IDK about excange.