Children do become citizens automatically if the following is also true:
1. Your child is under 18 years old, unmarried;
2. Your child has entered the U.S. and has lawful permanent resident status ("a green card");
3. Your child is residing in your legal and physical custody.
One key point is that if the parent that has become a citizen is the father, the child must have been born in wedlock or paternity of the child established before the child's 18th birthday.
These have been the requirements since February 27, 2001. They apply to natural born and adopted children.They do not apply to step-children unless the child is legally adopted by the U.S. citizen. In order for your child to obtain proof of their citizenship status, it is necessary to obtain a Certificate of Naturalization.
**Please note that these requirements are different than the rules that apply to children who are born abroad and acquire citizenship at birth because they have a U.S. citizen parent.