This is to corroborate my post No peace in Iraq since 1970s:
'Many Shī‘ī Iranians migrated to what is now Iraq in the sixteenth century. "It is said that when modern Iraq was formed, 75% of the population of Karbala was Iranian". In time, these immigrants adopted the Arabic language and Arab identity, but their origin has been used to "unfairly cast them as lackeys of Iran. Other Iraqi Shī‘īs are ethnic Arabs with roots in Iraq as deep as those of their Sunni counterparts.
...The Shia suffered indirect and direct persecution under post-colonial Iraqi governments since 1932, especially that of Saddam Hussein. Under Saddam public Shia festivals such as Ashoura were banned. It is said that every Shia clerical family of note in Iraq had tales of torture and murder to recount. In 1969 the son of Iraq's highest Shia Ayatollah Muhsin al-Hakim was arrested and allegedly tortured. From 1979-1983 Saddam's regime executed 48 major Shia clerics in Iraq. They included Shia leader Mohammad Baqir al-Sadr and his sister. Tens of thousands of Iranians and Arabs of Iranian origin were expelled in 1979 and 1980 and a further 75,000 in 1989. Shia opposition to the government following the first Gulf War was reportedly suppressed.'