For instance, the period between 1941 and 1945 was the last time the United States had been officially at war. Korea, Vietnam, Iraq (both times), and Afghanistan were merely prolonged cases of "military action" without actually declaring war on anyone.
for military action in Iraq (first gulf war) was Joint Resolution to authorize the use of United States Armed Forces pursuant to United Nations Security Council Resolution 678 on January 14, 1991, "Operation Desert Storm."
for military action in Afghanistan was House Joint Resolution 64 and Senate Joint Resolution 23, Authorization for Use of Military Force Against Terrorists
, Public Law 107-40, voted in by the US Congress on September 14, 2001.
for military action in Iraq (second gulf war) was on October 16, 2002, Operation Iraqi Freedom.
The Constitution gives Congress the power to authorized war, but doesn't require specific language. The words "declaration of war," do not have to appear on the resolution.