For a "roll your own" approach I use Pushover on iOS (I know people using PushBullet on Android) and then either use the Email->Push gateway and/or I have a simple bash script "push" that I can pass a subject and message so that I can very easily setup shells scripts to send me push notifications when they finish (great for long running processes that you might run in screen). All the time in a screen I will do something like:
cp /source/dir /target/dir && push "Moved" "Source Dir"
So that I'm not constantly checking screen or worse, forget about it and come back 1-2 days later.