When I was growing up, we were allowed to open one gift on Christmas Eve and the rest were opened on Christmas morning. When I was really young, Santa would wake us up (like we were ever alseep!) and give us the one gift.
For the last 14 yrs or so, my friend and her family come to my house to exchange gifts on Christmas Eve. We will also open one ore two of our own gifts. The stockings and other gifts are always opened on Christmas morning.
I have always put my son's big gifts out on Christmas Eve after midnight mass (while everyone sleeps). That way I didn't have to worry about him picking out a big gift for Christmas Eve.
This year is the first year my son doesn't do Santa

I still made him write a Santa letter though