About 8 years ago, I was singularly managing my company's email. When I was hired, they had been using an awful php based mail system. My first major upgrade was to start using Roundcube. This was a very, very early version and one of the first open source mail projects to offer 'ajax' functionality.
When Gmail for business became available, we migrated to that, but for a while Roundcube was the best web interface for email there was to be found.
Sadly I haven't kept up with the project over the years, but my early memories still serve me well and I hope that the project has gotten much better over the years.