Should children be included in wedding receptions?

After a recent question on whether not allowing children would impact the decision to attend, I wondered how common this is. I have never been to a wedding or reception where there were no children, I know when my parents went to weddings, I went along. It seems to me weddings are all about families, so this not allowing children thing is entirely new to me. I’m curious to know: is it common? Is it a good idea or a bad idea? How many weddings have you been to where children were not allowed/present? If a couple get an invitation that does not specifically mention their children or family should they assume children are not welcome?