The only thing the Constitution says about the subject is that "Congress shall have the power to... declare war." It doesn't give a specific format for an "official declaration of war" or anything like that. Congress hasn't declared an official war since World War II, but the actions in Iraq and Afghanistan were backed up by Congressional resolutions authorizing force against those regimes. Congress never declared war against Tripoli during the Barbary Wars (just 12 years after the signing of the Constitution) so at least historically it doesn't seem like the founding generation believed it necessary to pass some "official declaration of war" in order to signal Congress's approval for the President to execute war.
But previously, war meant some clear and present enemy like "Japan" or "Germany". Now the president has been given almost carte blanche access to fight a war on "Terror", a term so nebulous as to allow the president the right to do whatever he wants including spy on American citizens. While it's true Congress gave the president the ability to fight a War on Terror (or drugs or unicorns or whatever), it's the Congress who should be reining in that power when it gets out of hand. Instead they sit around and collect their checks.
I'm not as worried about an "official declaration of war" since the Constitution isn't clear on that need. I do wish Congress would grow a set of balls and do what's necessary to rein in presidential power regarding a ridiculous war on something we can't even see, much less defeat.
During the Iraq and Afghanistan wars, Congress authorized the use of force against the Iraqi government, and Al Qaeda and agents of Al Qaeda. I don't see how the latter is any more nebulous than Congress's authorization of force against the Barbary pirates in 1801.
I'm not talking about those wars. I'm talking about the War On Terror which was the genesis for spying on Americans. We don't have a war on Al Qaeda, we have a war on Terror. It doesn't get anymore nebulous than that. Neither Bush nor Obama would stand before the American People and say that the authorization of force in Iraq justified a sweeping surveillance program that includes American citizens. But the War on Terror enables them to do exactly that because of its murkiness. I don't blame either Bush or Obama for taking advantage of the power vacuum left by Congress in the War on Terror. I just wish Congress would take some of that power back.
It's well-established that Congress need not issue a formal declaration of war in order to authorize the President to use military force. Others here can probably speak better to why our Constitutional order evolved this way. My speculation has always been that many century-old laws are tangled up with special cases for times of formally declared war that are not suited to the era but too much trouble to excise.
Some would say that the lack of a formal structure of declaration of war, capitulation, occupation, and restoration of government is exactly what's been getting us in trouble and is a demonstration of what happens outside the bounds of legitimacy.
Congress hasn't declared war in ages.