I listen it from my friend. If there is a way to do it. I would like to know it.
Yeah, this is actually possible, but it depends on what router you have. Most home routers keep some kind of log, but honestly, it is pretty basic stuff. You might see which websites were visited and when, but the logs usually do not stick around for long. Maybe a few days or weeks max.
If you have a fancier router from your ISP or something business-grade, then you might get more detailed logs. But fair warning, digging through router logs is not exactly user-friendly. You need to access the admin panel and know where to look. Different brands put this stuff in different places. 
Mike is right about the logs being temporary. But here is something most people do not realize. If the websites use HTTPS (which is like 99% of sites now), your router will only see the domain name, not the actual pages someone visited.
So you might see facebook.com, but not which profile they looked at or what they posted. The whole thing is pretty limited compared to what people think they can see.
I tried this once with my Netgear router, and it was such a headache 
The interface looked like it was designed in 2005, and finding the logs took forever. Even when I found them, they were just a bunch of numbers and timestamps that barely made sense.
Unless you are really tech savvy, it might not be worth the trouble. There are easier ways to monitor internet usage if that is what you need.
If you really need proper monitoring, check out Xnspy. It works on phones and tablets, gives you actual browsing history without dealing with complicated router settings. Much simpler than trying to decode router logs. 
Okay, so I have been managing network stuff for years, and let me break this down properly. Yes, routers can log traffic, but there are serious limitations here.
First, storage space on routers is tiny, so logs get overwritten constantly. Second, encrypted traffic (HTTPS) means you only see domain names, not full URLs. Third, if someone uses a VPN, you see basically nothing useful, just encrypted gibberish going to a VPN server.
And fourth, the logs are usually formatted for machines, not humans, so reading them is painful. You would see entries like 192.168.1.45 connected to 142.250.185.46 on port 443 instead of John visiting YouTube.
If you actually need to monitor what someone is doing online, router logs are honestly the worst way to do it. They were designed for troubleshooting network problems, not tracking browsing habits.
Dan pretty much covered it all. I would add that some newer mesh systems, like Google WiFi or Eero, have better interfaces for seeing connected devices and maybe some basic activity, but even those do not give you a detailed history. They show you more like this device used 2GB today, rather than where that data went.
For anyone looking at this for parental reasons, Xnspy is way better than messing with router stuff. You can see actual browsing activity, apps being used, and it is all laid out in a normal dashboard. No need to be a network engineer. 
This whole conversation makes me glad HTTPS became standard 
Remember the old days when everything was just out there in plain text? Anyway, routers are not really built for this kind of monitoring.
They are meant to route traffic, not keep tabs on it. If you are trying to check up on your own network usage or maybe see if someone is hogging bandwidth, then yeah, router logs can help a tiny bit.
But for actual browsing history? Nah. You would have better luck just asking the person what they have been looking at online.
I have used both router monitoring and dedicated tools, and honestly, there is no comparison. Router gives you crumbs of information that take an hour to understand. Something like Xnspy gives you everything in five minutes, formatted in a way that actual humans can read. If you are serious about monitoring, use something built for the job. 