The only way my reading was monitored when I was a kid was my mum telling me to stop. I was always getting into trouble because I'd get so caught up in my book I wouldn't hear her calling me.
As for my kids, my son doesn't read. He used to read a lot, until he was about 11. He's 17 now. My daughter is 15. She went through a period of not reading for the last three or four years and has just started reading again this year. I keep an eye on what books she's reading, but I don't censor them. I know parents who read everything their kids read before they're allowed to read it. I couldn't do that. For one thing, I'd never get my own books read. And my kids would immediately turn down something mum's read.
I know we went to the library a lot when I was a kid, but I don't remember much about it. I can't remember if we were allowed to read adults books. I do remember they were on a completely different floor, so that did make them seem sort of off limits. At our library now we have different cards for children, teens, and adults. You can get any book on any card. Unless it's something with an age restriction like a movie or something, that's the only restriction I know of.