U.S. Citizens of any age, traveling outside of the U.S., are required to carry a valid passport (usually with 6 month validity remaining.) Learn more about required identification (there are ifs, ands or buts.)
Children under 18 years of age are not required to have ID to travel within the United States. All children, regardless of age, must hold a valid passport to travel internationally. Infants: One child over 14 days and under two (2) years of age, not occupying a seat, may be carried free of charge when traveling with an adult (12 years of age or older). Although a boarding pass is not required for the infant, you will need a Boarding Verification Document.
If a child (under the age of 18) is traveling with only one parent or with someone who is not a parent or legal guardian, U.S. Customs and Border Protection (CBP) strongly recommends that the accompanying adult have a note from the non-traveling parent (or, in the case of a child traveling with neither parent, a note signed by both parents) stating “I acknowledge that my wife/husband/etc. is traveling out of the country with my son/daughter/group. He/She/They has/have my/our permission to do so.”
CBP suggests that this note be notarized. If there is no second parent with legal custody of the child (e..g., the second parent is deceased, one parent has sole custody, etc.), relevant paperwork such as a court decision, birth certificate naming only one parent, death certificate, etc., would be useful as well.