From an Air Force web site:
The Air Force Cross is awarded to U.S. and Foreign military personnel and civilians who have displayed extraordinary heroism in one of the following situations: while engaged in action against a U.S. enemy, while engaged in military operations involving conflict with a foreign force, or while serving with a Friendly nation engaged in armed conflict against a force in which the United States is not a belligerent party. The Air Force Cross is awarded when the heroic actions fall just short of warranting the Congressional Medal of Honor.
Prior to 1960, when Congress established the Air Force Cross, enlisted men were decorated with the Distinguished Service Cross for heroic actions. In the Vietnam era, countless airman performed brave acts which were above and beyond the call of duty; however, of the enlisted airmen, only 20 were awarded the Air Force Cross. Since 1975, only one airman has earned the award, bringing the total to 21 recipients. The following section consists of brief, chronological accounts of these airmen and the heroic events which led to their decoration.