What do Brits think about the Royal Family and about Monarchy?

I'm not British, so it is very interesting for me. I can't imagine Great Britain as a Republic. I think there is a special charming in Monarchy. And in my opinion British Royal Family is the most famous of the Royal Families in the world. I heard that some British people are against the Monarchy and I don't understand why. Of course it's not my business, it's internal business of British people. But I'm very curious of it. So I will be grateful for your answers. And sorry for my mistakes in English.