I've worn compression socks since I tore my calf. I have a very understanding physio who recommended them so that I could run a 10k trail race about 3 weeks after I did it! They helped a lot, sort of holding everything in place so the scar tissue didn't get so sore so fast. I've just started running without them again as I'm back in Capris and I could feel where the tear was despite running pain free for a month or so in the compression socks.
I have a very experienced running friend who wears them after long runs to help with recovery (they help move the lactic acid from your calves by aiding blood flow I believe) but won't wear them for running as he says they make his legs feel heavy and slow.
I think I'm going to try a few months without mine and see how I go. The compression has come to feel very comforting but I'm going faster since I stopped wearing them so often. Not sure if it's training that's helping that or the socks. Need to do some test runs to check I think.