The Sadrists maybe the least understood of the Iraqi factions. They have a poor relationship with many of the other Iraqi factions, and recently come into armed conflict with the US. All this has lead to focus on demonizing Muqtada al-Sadr while ignoring the movement he is a part of.
The Sadrist movement began in the early 1990s following the first US-Iraqi war. There had been a history of conflicts between various Shiite tribal customs and the rulings of Shia religious leaders. In an effort to resolve this conflict Muhammad Sadiq al-Sadr (Muqtada's father) taught that tribal leaders should have the authority to administer religious law. (Sadiq al-Sadr is also the cousin or nephew of the early Al-Daawa leader Baqir al-Sadr who was killed by Saddam in 1979.)
Sadiq al-Sadr initially got the support of Saddam's Baath government eager to counter balance the power of radical religious leaders. However Sadiq al-Sadr began asserting his power against Saddam by the mid 1990s demanding the release of Shia scholars among other things. In February 1999 Sadiq al-Sadr and two of his sons were killed by Saddam loyalists. Muqtada al-Sadr his young son went into hiding along with many of his father's most loyal followers. There are rumors that SCIRI or Al-Daawa may have played a part in the killing of Muqtada al-Sadr. There are both rumors and an arrest warrant for Muqtada al-Sadr and others for the assassination of Ayatollah Sayyed Abdul Majid al-Khoei (I'm unclear which organization he was associated with). True or false, these rumors are a symptom of the conflict between the Sadrists and the other large Shia Islamists groups.
The Sadrists differ from SCIRI and Al-Daawa in ideology and demographically. The Sadrists are much more Iraqi nationalist wish to purge non-Iraqis (specifically Iranian and Lebanese) influences from the religious seminaries. They wish to create an Iraqi theocracy that will tolerate tribal customs and be independent of foreign (especially Iranian) clerical establishment. The Sadrists are concentrated primarily in the slums of Sadr city, though their recent defiance of the US has won them support even among some Sunnis. While Muqtada al-Sadr is a spokesperson and leader of the organization it isn't entirely clear how much decision making power he has vis-a-vis the other Sadrist leaders. Muqtada al-Sadr has said he is 30 years old in 2003, however other reports claim his age is as young as 23 or 25. It is also unclear if he has finished his clerical training. Due to both his youth and the movement's history with traditional Shia leadership he has not gotten much respect from them. The Sadrists hold no positions in the interim government.
Muqtada al-Sadr and the Sadrists came out of hiding after the fall of Saddam. They quickly asserted control of Sadr City (formerly Saddam City) getting to work repairing power and other basic services to the population there. The Sadrists maintain security and imposed strict Islamic law on Sadr City. Providing such repairs and social services has won the loyalty of many more in Sadr City. Gaining loyalty by providing social services has been a key factor in the growing of support for Hezbollah in Lebanon and Hamas in Palestine.
While Sadr has repeated call for immediate US withdrawal from Iraq, the US authorities initially ignored them as the Sadrists' strict security had been very effective at keeping Baath insurgents from operating in the area they controlled and the Sadrist stayed clear of US operations. This however began to change in April when the US authorities shut down his paper and arrested some of his close advisors. Protests and violent clashes with US troops followed. The Sadrist militia, Army of the Mahdi has taken control of many mosques and holy sites. The militia can be credited with both numbers and courage; but are neither experienced nor well trained. They have been much more successful at getting US troops to damage mosques and killing civilians than at inflicting US casualties. They are still learning to fight so they could easily become much more deadly in the future.
The exact relationship between the Sadrists and Iran is a subject of much speculation. The Sadrists are ideologically committed to an independent Iraqi clerical establishment and have criticized organizations such as SCIRI as agents of Iran. Recently there have been signs the relationship between Sadr and Iran is improving. Muqtada al-Sadr visited Iran in 2003 and spent time with Iranian leaders. While Iran does not give the Sadrists any official support an assortment of Iranian based Islamic charities have been funneling money to them in much the say way they funneled money to Hezbollah. There are also rumors that Iran has provided some training to the Army of the Mahdi but that is not confirmed.
The Sadrists are a wild card. They are the Shia religious faction with the most independence from Iran. They are also the Shia religious faction with the greatest desire to establish theocracy. Most worrisome the Sadrist are the most impatient of the factions.