I use Terminator locally and byobu on the remote servers.
Byobu is very convenient as also Matt Kurter said above. And very easy to learn because it uses the function keys to manage the split screens. So if you do not remember the correct key to press, you can just try. It is also fully customizable.
I need to use locally terminator because if I use byobu locally and I ssh to a server then it is not easy to manage two multiplexer one inside another.
If one has a clever solution for it, please let me know.