How to split terminal on remote server with background sessions

Screen

screen is a useful command to leave some processes running in the background on Linux.
We could actually split the screen terminal into sub-terminals with the following short-cuts:
(1) to split a terminal horizontally: press Ctrl+A, release them, press Shift+s
(2) to split a terminal vertically: press Ctrl+A, release them, press Shift+\
(3) to switch among sub-terminals: press Ctrl+A, release them, press Tab
But please note that the sub-terminals would be converted to background windows in screen if you detach (Ctrl+A+D) your screen session and then attach it again. To avoid this, you could use tmux instead.

Tmux

Tmux is more convenient than screen on this way.
type "tmux new -s sessionname" to create a new session
in the session, you could use:
(1) to split a terminal horizontally: press Ctrl+B, release them, press % (Shift+5);
(2) to split a terminal vertically: press Ctrl+B, release them, press " (Shift+');
(3) to detach the current session: press Ctrl+B, release them, press D;
(4) to attach to a session: "tmux attach -t sessionname";
(5) to switch to a pane: Ctrl+B, release them, press q (Show pane numbers, when the numbers show up type the key to go to that pane).

Reference:

http://fosshelp.blogspot.com/2014/02/how-to-linux-terminal-split-screen-with.html
https://www.youtube.com/watch?v=BHhA_ZKjyxo
https://gist.github.com/MohamedAlaa/2961058