I was recently copying some very large files from one remote machine to another. However, I had forgotten to use the nohup command and would need to leave before the transfer finished. Simple solution:

1) Suspend the process Ctrl+z
2) Background it bg
3) jobs to find the number to …
4) disown

Another problem that I ran up against was transferring large files and being disconnected. Since scp does not support resume, you have to use it in conjunction with rsync. Furthermore, the problem seemed to be an overload of a home router, so I needed to rate limit it. The final cmd:

rsync --partial --progress --bwlimit=500 --rsh=ssh orig_file user@host:~/dest_file