Iranian involvement in the Iraq War

The 2003 invasion of Iraq led by the U.S., which toppled Iraqi president Saddam Hussein and his Arab Socialist Ba'ath Party, was the decisive event that allowed Iran to begin exerting an unprecedented level of influence on Iraqi politics. Leveraging the fact that the regime change targeted a rival power and Shia Muslims accounting for the majority of the population in both countries, the Iranian government used Shia militias to serve its interests during the Iraq War.

Source: Wikipedia — Iranian involvement in the Iraq War (CC BY-SA 4.0)