Smotheroffive I know what their interests are and they are a talkative pair. A few keywords, plus I've worked out how they think, and hey presto, I find a Twitter account, etc. I follow them anonymously. They now know I do this, but so far they've only identified one twitter account I made. So they think that's it. 
(My boss also makes good use of my online finding of things.)
But we've had talks in the past, and I've so far not seen any indication of crap online behaviour. As they get older, and I see evidence of good behaviour, I withdraw from monitoring them. I don't look at my oldest's stuff now, she never gave any concern.
My youngest had an issue when he was about 9 or 10, he had a week or two of nightly sleepwalking and as he'd largely grown out of that I know something wasn't quite right. That's when I started the online checkups. Turned out he'd been watching Five Nights at Freddy's (kids version) but a couple of adult versions had made it through the filters and it had scared him enough to restart the sleepwalking. It seems all the boys in his class had been watching it.