When Saddam was removed from power the US took temporary charge of Iraq.
In June 2004, the US gave up control, instead choosing a prime minister and president to take charge of a temporary government.
The Iraqi people finally got to choose their own politicians in December 2005, voting for the people they wanted to be in charge for the next four years.
The people who make up the government - called the cabinet - were finally approved in May 2006 after a lot of disagreements.
The prime minister is called Nouri Maliki.