I've looked through the router settings and I can't see an ability to monitor which sites are being visited. I do see the Parental Controls but that only blocks sites a parent already knows about. Also, I have tried to block two websites across the whole network with Website Blocking but it doesn't work.
Most routers will not have the feature to monitor what is being accessed. You need something more enterprise grade for that. You'll also find most kids can get around parental controls also. You could try installing software on your kids computer to monitor what they access but you still won't be able to block everything. If it's a tablet or phone, then it's much harder.
There are countless sites out there that have content that parents may object to their kids seeing. Depending on the age of your kids, they may have already seen some of that content as well, either at home or elsewhere. Often the best courses of action if your kids are old enough is to discuss inappropriate content with them, why they shouldn't be looking at it, and consequences if they do.
Thanks Nighthawk. My situation is more complex. The situation is a child accessing online content that is harmful to their mental health and they don't have the maturity to honour a promise not to visit those sites.
@Blorchito Your between a rock an a hard place. But is it not possible to do this on their search engines (google - firefox). They would probably sort the that out quickly. The internet is available all over the place maybe try to talk to a person that has good programing knowledge. I don't have your worry so good luck. Polecat
You might need to seek tools on the device itself, rather than the modem. There are a variety of child-minding software applications which may better meet your needs.
Like @polecat said, you're likely looking for more of a monitoring setup, which is not typically built into a router. You can have the ability to blacklist and whitelist sites, but if you need to see a record of sites, you need something that can full on track that data. Depending of if you're using Windows or a Mac, you might be able to set up some sort of mobile device management so you can track it, but that would take a bit of work on your part.
This website has a list of some options (though I cannot speak to their quality): https://famisafe.wondershare.com/parental-control/computer-monitoring-software-for-parents.html
Another option - if your child is using an iOS devices (iPad or iPhone) you could set it up with parental controls and put heavy restrictions on what sites they can visit, whitelisting things as they need. https://support.apple.com/en-ca/HT201304