During World War II, the United States Army divided its operations around the world into four theaters. Forces from many different Allied nations fought in these theaters. Other Allied countries have different conceptions of the theaters and/or different names for them.
Operational command SHAEF
Normandy Campaign June 6, 1944–July 24, 1944
Northern France Campaign July 25, 1944–September 14, 1944
Rhineland Campaign
Lorraine Campaign (unofficial) September 1, 1944–December 18, 1944
Ardennes-Alsace Campaign December 16, 1944–January 25, 1945
Central Europe Campaign March 22, 1945–May 11, 1945
Operational command AFHQ
Algeria-French Morocco Campaign November 8, 1942–November 11, 1942
Anzio Campaign January 22, 1944–May 24, 1944
Egypt-Libya Campaign June 11, 1942–February 12, 1943
Naples-Foggia Campaign
North Apennines Campaign
Po Valley Campaign
Rome-Arno Campaign
Sicily Campaign
Southern France Campaign (One month after the invasion, command was passed to SHAEF and the European Theater of Operations)
Tunisia Campaign
Operational commands were the Pacific Ocean and South West Pacific.
Pacific Ocean Areas (command) - Chester W. Nimitz
Pearl Harbor
Doolittle Raid
Coral Sea
Midway
Solomons
Aleutians
Gilberts & Marshalls
Marianas & Palau
Volcano Is & Ryukyu Is
South West Pacific Areas (command) - Douglas MacArthur
Guadalcanal Campaign 1942–43
New Guinea Campaign 1942-45
Philippines Campaign 1941-42
Dutch East Indies campaign 1941-42
Solomon Islands campaign 1943–45
Guadalcanal Campaign 1942–43
Battle of Timor 1942-43
Philippines Campaign 1944–45
Borneo campaign 1945
The China Burma India Theater served more as an Administrative Command rather than a Theater of Operations and lacked any true Operational Command.
The Operational Command was joint Allied South East Asia Command in the South-East Asian Theater The American General Joseph Stilwell commanded the operational Northern Combat Area Command and used his other positions to communicate directly with Joint Chiefs of Staff about some operational matters.
Burma Campaign
Burma 1942 Campaign January 1942 – May 1942
Central Burma Campaign
China Defensive Campaign July 4, 1942 – May 4, 1945
China Offensive Campaign May 5, 1945 – September 2, 1945