What were the wars that took place AFTER the cold war?

Well, there was a rebel conflict between Somalia and the US which took place in 1991 (end of the Cold War) and has been going on ever since.
In 1998 a terrorist organisation called Al-Qaeda began a serious of bombings on American territory such as the USS Cole and a US embassies in South Africa.
Then in 2001, Al-Qaeda's leader Osama Bin Laden, arranged a terrorist attack on the World Trade Centre resulting of the deaths of almost 3,000 innocent civilians.
Almost a month after this attack George W Bush launched Operation Enduring Freedom which resulted in invading Afghanistan and other Islamic nations.

They're goal is to remove all of Al-Qaeda forces.

The UK and some Russian and the Afghan National Army are also helping the US achieve this goal.