They don't really support IMAP -- they have an IMAP bridge which you have to run on your local machine (it doesn't support Linux -- they say they have a beta version but I don't think it's public and it's been "in beta" for a few years). This also means you can't use your own client on your phone because there's no bridge for phones (and their clients are all proprietary, with seemingly empty promises to make them open source "soon" several years ago).
They also don't support sending plain-text email (a bit of an odd restriction, and it means most mailing lists will drop your emails -- making it unusable as a primary email service if you use mailing lists often).
In addition much of their "secure email" features are only super useful if all the recipients are using ProtonMail (they use PGP under the hood, but all the keys are managed by ProtonMail -- though encryption is done client-side). You can set up a symmetric encrypted email for non-ProtonMail users, but that basically gives the user a link and they have to enter a password you've given them over a different secure channel (making it little more than a nice interface to gpg --symmetric).
All-in-all while ProtonMail is nice, for my usage it wasn't workable. I ended up using Mailbox.org which is a more traditional email system (though they have a cool feature where you give them your PGP public key and they will encrypt all plaintext emails they receive so that they are all encrypted when stored both remotely and locally).