My broadband blinked out for a few seconds this afternoon, the way it does, and three months ago that would have cost me a long-running job and a fair bit of swearing. Today it cost me nothing, because the work was inside tmux on the remote host and not tied to my fragile connection home.
That is the whole pitch. tmux runs the shell on the server, detached from your SSH session. The connection drops, the session keeps running. You reconnect, type tmux attach, and everything is exactly where you left it: the half-finished build, the tailing logs, the editor you had open. The terminal becomes a thing that persists rather than a thing that evaporates the moment the network coughs.
I resisted it for years on the grounds that I already had screen, and ctrl-b instead of ctrl-a felt like learning to write with the wrong hand. It was worth the week of fumbling. The split panes are genuinely useful, but they are not why I keep it. I keep it because a dropped connection is now a shrug and a reattach, and a long job started over SSH no longer needs me to sit and pray the link holds. Start it in tmux, detach, come back when it is done.