Later, as occupied territories were recaptured, they were always there. They fought as far up as Mosul and beyond to Tel Afar. Some of their supporters and admirers emphasise the difference between them and the "politicians" and "army generals". Members of the latter groups, they say, did nothing but stuff their pockets with cash and run away from IS. There have also been intermittent accusations that they were to blame for the emergence and spread of IS.
The pro-Iranian "Conquest Alliance"
The extent of these militia leaders' political influence is unclear. But many observers assign them considerable significance. Nevertheless, not all groups under the PMF umbrella have developed political ambitions.
Many have responded to an appeal by senior Iraqi clerics, who say politics should be left to the politicians. One of these clerics is Ali al-Sistani, Iraq's top Ayatollah.
But the pro-Iranian militias, who pay more heed to Ali Khamenei in Tehran than to Sistani in Najaf, are pursuing political goals. Under the leadership of Hadi al-Ameri, they have formed a political alliance: the "Tahaluf al-Fatah", the Conquest Alliance.
One of its members is the Badr organisation led by Al-Ameri. Others include several pro-Iranian groups such as "Asa'ib Ahl al-Haqq" and "Kata'ib al-Imam Ali", known for their fanatical partisan support for Iran.
The "Citizen Alliance"
A further grouping that has thus far adhered to the same movement, has split off from the Conquest Alliance. This is the group originally formed by the cleric Abdul-Aziz al-Hakim. It used call itself the SCIRI ("Supreme Council of the Iraqi Revolution in Iran") and fought on the side of Iran in the Iran-Iraq war from 1980 to 1988.
Abdul-Aziz al-Hakim died in 2009. His son Ammar al-Hakim has now separated the group from Iran. He named it the "National Wisdom Movement" and built up his own alliance: the "Citizen Alliance".
Iraqi political parties are generally small. Often, they are basically made up of the supporters of individual influential figures. Alliances are therefore crucial. 238 parties are enrolled for the approaching elections. Of these, 143 have joined forces to form 27 different alliances, which have in turn registered for the poll. These alliances put up joint candidate lists. Voting is to take place in 18 of the nation's provinces. Each province forms its own electoral district.