I am assuming small children, maybe 6-10 years.
EDIT: I missed the toddler
tag. I will let this answer stand as it is for the time when your children are 6-10 years old. I would strongly suggest to never ever let toddlers (1-3) view Youtube alone.
Technical answer: Linux solution
My kids watch Youtube, how to monitor what they see?
I did that myself for a while. I installed a Linux machine which acted as enforced http proxy for her windows machine. To do that:
- Install Squid on the Linux machine.
- Configure your internet router so her Windows PC cannot access the internet directly.
- Configure the Windows PC so it uses the Linux machine (squid) as proxy.
- Configure squid to log all accesses.
Hence I had a log of all URLs she ever accessed. Then I wrote a little script which parsed that log file, looked at all Youtube URLs, added the titles of the respective videos, and sent all of that to a handy HTML page. We now have a HTML page per day with video title + link, which can be quickly checked if in doubt.
Note that depending on your country you better tell the other person that you are regularly monitoring them...
Note: this worked a few years ago. These days, Youtube uses SSL and the video URLs are no longer visible to a normal proxy. This means that today one would need to get more creative - create a man-in-the-middle situation, or try to configure a true reverse proxy with no SSL "inside". I have not tried this and do not know if it is possible, or how effective Youtube is for enforcing its SSL. So, as of 2016, take this recipe with a bit of salt.
Parental answer: maybe?
I think it is not a good idea to give young children full freedom and then have nagging doubts every day. Especially if I would see my child quickly close browser tabs / clear browser history everytime I enter the room, that would be an absolute no-no.
No matter what kind of content they can find online, the much more important issue is trust between you and them.
It must be 100% clear that they can do what they do because you trust them. So you must have a way to let them know what the boundaries are, and you must feel like your trust is justified. The moment they cannot convince you that you can 100% trust them, it must be over.
So, if you are maybe not so technically inclined, do yourself a favour, and handle this like every other parenting issue. If they are not able to freely and happily chat with you about what they have youtube'd today, then they have no place using YT on their own. If you find them obviously uncomfortable when you enter the room while they YT, then it should be over, really.
I did what I did because I had the Linux box and Squid already in place and was whitelisting the websites she could watch alone (plus the server was on at certain times per day also, so there was no fighting about that either). Youtube came relatively late, and I mainly wanted to check for major problems; I relatively quickly got rid of my special Youtube script because everything seemed to be quite OK, and I saw no reason for further monitoring. She of course knew from the start that I was doing it, and it was no problem for her.
I try every now and then to see what they are really looking at but many times they wander to some video I think it's not suitable for them like amateur cartoons with scary faces and stuff like that.
Well, you have to ask yourself how much "not suitable" that is. Cartoons with scary faces might be borderline; what about videos with mutilations, corpses, racist stuff, subtle psycho horror movies or just random bullsh*t? I would certainly not want them to see that everytime I leave the room.
Check the browser history together
A mixture of both approaches: have regular sitdowns with your children, and go through their browser history together. Let them tell you what they liked best, re-watch some clips together, maybe. If you see some that you find unwholesome, tell them that they should not watch that anymore.
If you do that, and find an erased browser history, you know what that means...