Tmux has replaced a long time ago our use of screen to handle persistent sessions on remote servers and also more powerful terminals on our work stations.
Tmux is powerful, it has a few downsides (ssh agent, copy paste, ...) but overall it can really make a terminal a lot more productive.
Creating a tmux session is easy :
tmux, the basic shortcuts to know are "Ctrl b + c" to create a new window, "Ctrl b + n" to jump to the next window and "Ctrl b + d" to detach.
To reattach running
tmux attach is the one to use.
The next level after different windows is using splits : "Ctrl b + %" create a vertical split in the current frame, "Ctrl b + " " (yes that a double quote) will create an horizontal split.
To jump between splits you can use "Ctrl b +
Finally the last tip is about how to type at the same time in all the splits. While running tmux and with 2 or more splits open you can type "Ctrl b + :" (to go on the tmux command) and type : "setw synchronize-panes on" (and the same with off when you are done). And then everything you type in one frame will appear in the other ones. Very practical to synchronise your actions across several hosts.