Fresh research shows most parents have no idea what their children are doing online.
Internet security company Norton surveyed more than 600 people who had children under 16.
The survey found 74 percent of those questioned were oblivious to their children's online lives.
Half of those surveyed said they had never discussed cyber bullying with their children.
Technology strategist at Norton, Mark Shaw, said the survey showed many people were not doing enough to keep their children safe online.
He said parents talked to their children about keeping safe in the physical world, and they needed to start talking about cyber safety too.
Mr Shaw said children were interacting online more and at younger ages, and were vulnerable to abuse at any moment.
Netsafe executive director Martin Cocker says parents probably did not need to be informed of their 16-year-old's online activities as much as with an eight-year-old.
He said parents should not be intimidated by their children's online prowess and should have conversations about internet safety.
"Our advice is for parents of younger children to stay across what's going on, to sit alongside their children when they get a chance, talk through the things they're doing, so that by the time that they're teenagers you're confident they know how to manage the challenges that they face.