Several commenters are asking what mosh provides that's better than ssh+screen/tmux.
A few years ago I spent a summer at a remote field site, sharing a flaky T1 with 100 other people over equally flaky site-wide wireless network. (Many of those people were undergraduates who had been politely asked not to use the research network to access facebook, but, well, you know.) Not only was packet loss common, but latencies to an outside host varied whimsically from 50ms to 2000ms. In those conditions ssh was unusable, tmux or not. I was able to do work on remote servers only because of mosh.
Let me clarify a little more. Mosh hides latency by doing display prediction. It guesses what the results of your keystrokes will be and displays them locally, highlighted as predicted with an underscore.
A few years ago I spent a summer at a remote field site, sharing a flaky T1 with 100 other people over equally flaky site-wide wireless network. (Many of those people were undergraduates who had been politely asked not to use the research network to access facebook, but, well, you know.) Not only was packet loss common, but latencies to an outside host varied whimsically from 50ms to 2000ms. In those conditions ssh was unusable, tmux or not. I was able to do work on remote servers only because of mosh.