The War on Terror may be said to have begun officially after the attacks on the World Trade Towers, known throughout the world by the numerical acronym 9/11. It took very little time for the Bush Administration to identify the supposed culprits and then to attack the Taliban in Afghanistan.
The putative reason to attack in Afghanistan was to rout Al Qaeda from Afghanistan. Al Qaeda means "list" in Arabic and the CIA helped form Al Qaeda when Afghans were fighting the occupation of the USSR. There is considerable controversy over whether Al Qaeda existed at the time of 9/11 and, if it existed, whether it was in some sense a captive client of the CIA, which had helped create it.
The same argument can be made for Osama bin Laden himself who, skeptics claim with considerable evidence, was a CIA asset. There is no doubt in fact that bin Laden had a relationship with American intelligence during the time of the Russian invasion of Afghanistan, for the CIA apparently supplied weapons and training to bin Laden and the troops he was leading against the USSR.
There is no evidence today that bin Laden is alive, and newspaper articles in Egypt and Pakistan reported on his funeral in December of 2001, but it is fairly clear that the audio and video tapes that purport to have been from him are in some sense phony, that is, derived from other tapes and videos made prior to 2000 and recombined. It is said, most notably by Dr. Sanjay Gupta on CNN, that bin Laden suffered from advanced kidney failure; the odds of him being alive ten years post-9/11 are probably infinitesimal.
Al Qaeda itself remains swathed in mystery. The US war on Afghanistan was supposed to drive Al Qaeda from Afghanistan but the war grinds on even though there are supposedly only minimal numbers of Al Qaeda left in Afghanistan. It is said that Al Qaeda has taken shelter in parts of Pakistan and elsewhere, but there seems little evidence of that as well. Many of the famous Al Qaeda terrorist attacks that have taken place in Europe and America have been shown to include considerable FBI involvement and could be considered entrapment.
The CIA apparently helped create Al Qaeda. Today, there is little evidence of Al Qaeda activity and even less significant evidence of its continued existence as a formal, independent fighting force. Its terrorist efforts are often accompanied by significant Western intelligence involvement. Given these circumstances, the idea that the West and especially the US is fighting a worldwide "war on terror" is increasingly doubtful. There are "bad guys" in the world that the West intends to face down. But Al Qaeda, as a formal entity, appears less and less to be among them.