There have been no declarations of war by any UN members since it was created October 24, 1945. Formal declarations of war for all UN member states is illegal. Only the UN Security Council has the legal right to authorize force in response to an aggressor. That's why the war in Korea was called a "police action" and executed under UN supervision.
Vietnam was an attempt to aid the current government there to fight Communist takeover of the country. It began for the US by sending advisers only. When China became involved, the US started becoming operationally involved. We never declared war there partly because we were effectively fighting the Chinese, not N. Vietnam.
As a result of the unprecedented escalation in Vietnam, The War Powers Act of 1973 puts limits on the ability of the President to send American troops into combat areas without Congressional approval. Under the act, the President can only send combat troops into battle or into areas where ''imminent'' hostilities are likely, for 60 days without either a declaration of war by Congress or a specific Congressional mandate. The President can extend the time the troops are in the combat area for 30 extra days, without Congressional approval, for a total of 90 days. The act, however, does not specify what Congress can do if the President refuses to comply with the act. Congress could presumably suspend all funds for such troops and override a Presidential veto.