Sieve is pretty cool; it runs user-defined scripts server-side, on delivery to addressee's mailbox. The scripts are in the Sieve language, which is just for mail filtering. But it's a bit abstruse - it may be rudimentary, but most users don't want to tangle with a language at all.
Anyhow, the Roundcube UI includes natively a Sieve script editor made up of drop-downs, which makes it much clearer what filter-steps you're asking for. I'm rather minimalist; I prefeer Squirrelmail, if I have to use webmail. But this feature of Roundcube is really good.
This means that you don't have to synchronize your filters between mobile client A, laptop client B, webmail client C. Thy're all on the delivery server (which is usually the same as your IMAP server). The filtering happens before you log in to email, and before your client knows there is an email.
Sieve is a specification, not a product (and not some specific PHP script). It's part of the Dovecot package in the Debian distro. It's client-server, only because there is a protocol for a client to upload/update scripts. So there's a wire protocol for management. But it has nothing to do with retrieving mail. Sieve on the server only affects what happens on delivery.
I think Sieve is totally the sanest way to do per-user mail fitering.
I was thinking of stopping to use gmail and hotmail, and run my own webmail client on a droplet. I don't like the idea of all my documents being tracked. Is there anything that competes with them that I could deploy.