The United States Presidential Unit Citation is "awarded to units of the Armed Forces of the United States and co-belligerent nations for extraordinary heroism in action against an armed enemy occurring on or after 7 December 1941. The unit must display such gallantry, determination, and esprit de corps in accomplishing its mission under extremely difficult and hazardous conditions as to set it apart and above other units participating in the same campaign. The degree of heroism required is the same as that which would warrant award of a Distinguished Service Cross to an individual." 
The Army citation was originally established as the Distinguished Unit Citation on 26 February 1942, and received its present name on 3 November 1966. All members of the unit may wear the decoration, whether or not they personally participated in the acts for which the unit was cited.
For the Army, the emblem itself is a solid blue ribbon enclosed in a gold frame. The Navy version has blue, yellow, and red horizontal stripes.
The Republic of Korea Presidential Unit Citation is similar to the US decoration, but is awarded by the Korean government. In appearance, it is mostly white with a taeguk (yin-yang symbol) in the center, enclosed in a gold frame. 
The Philippine Presidential Unit Citation was awarded by the US government to certain units serving in the Philippines during World War II, and also for service to the Republic of the Philippines during natural disasters in 1970 and 1972. In appearance, it consists of three equal strips of blue, white, and red, in a gold frame. 
The Republic of Vietnam Presidential Unit Citation was awarded by the Vietnamese government to all personnel in the Military Assistance Advisory Group during August and September 1954. The emblem consists of three vertical red stripes on a golden yellow background, in a gold frame.