The National Collegiate Athletic Association announced a ban on composite bats in 2009 and the National Federation of State High School Associations did so in 2010.

WSJ: Little League Bans Composite Bats

Among the organizations with full or partial bans of composite bats: Little League International, Babe Ruth League, the National Federation of High School Associations, and the NCAA. In most cases, if a bat meets certain standards basically, not having any more pop than a wood or aluminum bat it will be allowed.

FORBES: Composite bat bans have sporting goods industry crying foul