A quick recap. Back in 1990 Iraq president Saddam Hussein noticed that his neighbour to the south, Kuwait, was encroaching by moving the rocks that marked the border, and was also helping itself to Iraqi oil by means of some creative sideways drilling from their side of the border. Saddam resolved to teach the tiny nation a lesson by annexing it. Being a cautious fellow he checked out his plan with the Americans first.
US ambassador to Iraq April Glaspie was dully consulted and advised that the USA was unconcerned about Arab-on-Arab conflicts and gave him the green light (the go-ahead coming originally from her boss Secretary of State James Baker.)
So in August 1990 Iraqi troops entered Kuwait and had conquered the whole country a few hours later.
At which point the then world's bigger oil producer Saudi Arabia caught fright thinking they were next on Saddam's list and persuaded US president George Bush Snr to kick the Iraqis out of Kuwait. A coalition of 34 nations was put together and a big military presence was built up in Saudi. This was called Operation Desert Shield.
Iraq was attacked from Saudi in Operation Desert Spear. Needless to say the Americans (with a bit of British and other help) won easily. This was Gulf War I. It cost $60bn, and most of the cost was paid for by Saudi Arabia. Saddam was left in office as president of a much weaker Iraq.
This war could generally be considered "a success". The mission objective was achieved. Someone else paid most of the bill.
President George Bush Snr only got one term in office and was succeeded by Bill Clinton at the start of 1993. Clinton had his problems in office (the Oval Office mainly) but he didn't actually declare war on anyone and served two terms as president, ie until January 2001.
George Bush Jnr, "Dubya" to his friends, son of the previous President Bush, was "elected" president in 2001, despite receiving fewer votes than his rival Al Gore - for a month or so no-one really knew who had won. Nine months into Dubya's presidency nine-eleven happened and America went to war in Afghanistan. By 2003 Afghanistan was deemed done and attention turned back to Iraq.
By this time Tony Blair was PM in the UK and was getting on quite well with Dubya. Dubya seems to have decided to pick up where his pa left off and have another crack at Saddam. Blair, playing the Thatcher role, was right behind him. Some dodgy dossiers alleging that Saddam was building "Weapons of Mass Destruction" were downloaded from the Internet and published far and wide. The British parliament voted; the UN security council voted; and before you know it Gulf War II was born.
Gulf War I was reactive to Iraqi actions; albeit actions the US had originally condoned.
Gulf War II was more of a: let's have a war and think of a reason afterwards. Both the main players, Dubya and Blair, were walking in the footsteps of previous leaders much greater than them: Dubya, his father; Blair, Mrs Thatcher. This was a war born out of the insecurity of two of the most powerful men in the world.
Thus in March 2003 Operation Iraqi Freedom began. Half a million Iraqis were killed and the basic invasion was over by April. Saddam ran away (he was captured in December that year and executed in 2006) Baghdad was taken and statues were toppled. However American and allied forces were kept busy in Iraq dealing with insurgencies until 2011, ie Dubya never finished the job and left it as work-in-progress for Obama who took over in 2009.
Saddam Hussein was not a strongly sectarian leader. His regime was essentially Sunni but he had Christians in his government, and even women.
After the invasion the Americans ran the country by decree for a year, during which time they passed laws allowing "foreign investment" ie asset stripping, and granting immunity from all civil and criminal court actions for foreign contractors.
Then a Shiite called Allawi was elected prime minister. He lasted a year and was succeeded by another Shiite called al-Jaafari , who, topically, was educated at Mosul university. He lasted a year and then al-Maliki, also Shiite, took over in 2006.
Meanwhile all the Sunnis Saddam used to employ as army officers, civil servants and the like, were out of work and feeling the odium of being an oppressed minority. However, since Iraq is a Shia majority country there hasn't been much they can do about it.
It has to be said that al-Maliki has not attempted any sort of inclusive or conciliatory government. All his appointments to high office have been Shiites. He has openly hob-nobbed with the Shiite elite in Iran.
Now it seems the Sunnis have finally got their act together to do something about this "unfair" situation. Sunnis are 70% of all muslims. Al Qaeda is Sunni. The Saudis are Sunni; 99% of all muslims in the UK are Sunni. So the new kid on the block, Sunni ISIS, can expect money to be lavished on it, and foreign fighters to come flocking to its banner.
This is where it all gets a bit confusing. The Saudis would naturally like ISIS to take over in Baghdad. The Saudis have major behind-the-scenes pull in America. Taking the US presidency requires money and money comes from Saudi. Bushes Snr and Jnr were both "oil men" ie, beneficiaries of Saudi largess. But Obama is more of a Israeli pawn, and he will be in office through the end of 2016. So the strong Sunni alignment isn't there. It looks like even the Shiite mother ship Iran is coming in out of the cold. The old instinctive animosity isn't there at the moment. (Iran has been PNG to America since the CIA-employed Shah was kicked out in February 1979. The embassy hostage crisis of November 1979 didn't help.)
At the moment, the Americans don't care if a Shiite regime runs Iraq. The media offensive to build up ISIS leader Abu Bakr al-Baghdadi as a major villain in the mould of Saddam Hussein or Bin Liner hasn't really got any steam behind it and the American sheeple have not been revved up to get boots on the ground. The Saudis aren't getting traction with the White House and Israelis don't care enough to make anything happen.
So Gulf War III? Mainly a low-key affair consisting of drone strikes and persuading other countries to do the grunt work and accept the inevitable body bags.