Pediatrics is the branch of medicine that involves the medical care of infants, children, and adolescents. The American Academy of Pediatrics recommends people be under pediatric care up to the age of 21. Pediatrics is the branch of medicine that involves the medical care of infants, children, and adolescents. The American Academy of Pediatrics recommends people be under pediatric care up to the age of 21. Pediatrics is the branch of medicine that involves the medical care of infants, children, and adolescents. The American Academy of Pediatrics recommends people be under pediatric care up to the age of 21.