There are two schools of political theory in the Twelver sect of Shia Islam. The Twelver sect is the dominant sect in Iraq and Iran (and other countries in the Gulf). One of these political schools is in power in Iran and is the Khomenist School. This school believes that the government is run by the clerics and so the clerics have executive power in Iran. The other school is the Quietist School headed by Ali Sistani of Iraq. This school thinks that the jurisprudence of a government should be run by the Clerics, or at least that the Quran is a leading text of jurisprudence, but that the executive is a secular function.
Since the invasion and introduction of democracy in a Quietist fashion in Iraq, there has been a lot of clerical travels between Najaf, Iraq and Qom, Iran. Qom is the spiritual center of Iran. The Quietist school has been gaining significant ground against the Khomenist School in Qom and the real struggle in Iran is between groups of clerics over who will run the government.
This is a non-trivial result of the invasion of Iraq, and it's true long-term objective, IMHO.