Mum-of-four Alex Merton-McCann is one of those parents and says cyber safety is something her family deals with every day.
"My children, like all children of their generation, live and breathe their life on the internet and we try very hard to get them off, but there is such a draw there for them," says Alex.
"My 13- and 15-year-olds are the ones that I have to be even more vigilant about. They are on Facebook, they're on Skype, they're on forums, they buy things online very regularly; their life is online."
Sydney-based Merton-McCann, whose other children are aged eight and 10, believes it is her job to make sure they stay safe.
In 2011 she set up the blog secretmummybusiness.com because she wanted to create an online community that could discuss cyber safety issues.
"I just felt like I could give back and provide a bit of a community for mothers that otherwise probably wouldn't have an opportunity to chit chat to people because their lives are so busy," she says.
With about five years experience in the technology industry, she seemed the right person to help. She also blogs about online safety via security technology company McAfee Australia's website (mcafee.com/cybermum) and says the biggest concern most parents have is stranger danger.
"I know my eldest children regularly get (Facebook) friend requests from people they have no connection with, who don't even live in the country, so that is something that's a really big issue for me and fellow mums," she says.
There are also concerns about the time kids spend online and Merton-McCann, 40, says parents should consider putting time limits in place.
Inappropriate content is another cause of worry, particularly among mums and dads with primary school-aged children.
"Kids are inquisitive. They hear words that they wonder about and typing something into a Google search will bring them all sorts of wondrous visual rewards so that's a really, really big concern."
So what should parents do? Merton-McCann's first tip is to set up the family computer in an open spot in the home.
"Put it where there is a high traffic area where you can walk past, you can peel the carrots and see what the heck's going on. It's so important."
Also, she says, sit down with your children, especially those who are teenagers, and explain the risks.
"Don't sugar coat it too much. Explain how it works so you can pre-empt a problem. Outline how you want them to behave online; the concept of respect, public soap-boxing, what's appropriate, what's not .."
Having a two-way dialogue with your kids is the key, she says, along with making sure they know they can come to you if something goes wrong. This applies particularly if you find that your child has been visiting inappropriate sites or become friends with someone thought to be suspicious.
Cyber risks should also be explained to pre-teen children but perhaps in less detail, says Merton-McCann, and with more of a focus on stranger danger.
In regards to Facebook, she says the social networking company is very responsive to concerns, however she believes education is the best route.
"I think you just need to explain to your kids to de-friend that person. You explain the risks and you sit down and you just say: 'Look, I'm not trying to be big brother; my job is to catch you when you fall. We need to prevent issues, we need to nip them in the bud and this is how you need to act.'"
Keeping up to date with the technology children are using will go a long way to earning that child's respect as well, she says.
Parents can also buy security software to block certain sites on their home computer and even on their children's smartphones.
But again, not everything can be monitored and Merton-McCann reinforces the importance of children learning about what constitutes appropriate behaviour.
Teach your children about internet etiquette and how to deal with online bullies, she adds, and instil in them the need to respect their peers and look out for their mates.
But finding that balance between allowing kids to be part of the online community while also feeling confident they won't be targeted by people with ill intentions is difficult, Merton-McCann admits.
Her advice is to put rules in place.
"I think you need to say to your kids first of all 'you can't spend all day online'," she says. "Work out what works well for your family."