A while ago I wrote about notmuch and astroid as an alternative to mu/mu4e. Since then lots of folks have told me how much they love notmuch and what a great solution it is for email. There’s even an Emacs client.
I’m very happy with mu and mu4e and don’t have any urge to try something else but if they don’t work for you or if you aren’t an Emacs user, notmuch may be a good solution. It works with Mutt, has its own Emacs client, and, of course, works nicely with Astroid. If you’d like to know more about notmuch, Carl Worth, the notmuch developer, has a video that explains its rationale.
As far as I can see, notmuch and mu are pretty much similar except for tags. Notmuch uses tags as one of its principal organizing methods in addition to search. You can, if you like, essentially recreate a folder structure using tags but I’m not sure why you’d want to. Mu, on the other hand, doesn’t really support tags. You can add a tagging function similar to Gmail but there’re apparently problems with Email servers that aren’t Gmail. In my experience, searching is really all you need, especially since the searching in both applications is excellent and fine grained.
The video is from 2011 when notmuch was still young so there’s been many improvements since then but it’s still useful for giving you an idea of what notmuch can do and why Worth developed it. The video is about 45 minutes long so plan accordingly.