Update: Folowing some of the comments, I tried tmux and compared to GNU Screen it indeed has more features and is properly maintained.
If you've ever had to do anything in the terminal/console/command line for a longer time and especially on a remote host, you've most probably used screen already. In its most basic use it is a tool to create a pseudo TTY session, which can be detached from a TTY session (real or pseudo), running in the background and reattached later on in a different TTY/PTY or even over SSH.
So GNU Screen solves the problem of running sessions or timely processes, when you need to log out or access the same session from different devices.
If you're at least a bit like me, ocasionally you might forget to run something in screen and only remebered it would be nice to be able to detach it from the current TTY/PTY. Luckily there's a few tools that can detach a process from one TTY/PTY and attach it into another (e.g. into a screen session). From what I could gather Reptyr is probably the best one so far.
Both tools are in Portage so you can easily just install them by:
emerge screen reptyr
hook out → whew, finally the madness of my recent system update is over
P.S. If you don't like Screen and Reptyr, there's also other similar tools out there.