Strategypage looks at Iraq, with a short look at Syrian Kurds:
The government has a hard time getting everyone to agree on who the most urgent future threat is. Iran is the most frequently mentioned threat, the one that even many Shia Iraqis regard as a neighbor more interested in subjugating than supporting Iraq. But Iran is also the neighbor with the most armed and organized local support inside Iraq. One side effect of this is that Iraqi leaders still support links with Saudi Arabia, Kuwait, UAE, Turkey, Jordan and the United States.
On the issue of Iranian influence in Iraq, yes it is there. But most Iraqi Shias reject Iran. Add in the Sunni Arabs and Sunni Kurds and that is a potentially decisive coalition. But those who support Iran are armed and dangerous. And the anti-Iran coalition is shaky and vulnerable to Iranian measures to divide and conquer.
But America's defeat of Saddam in 2003 did not cause the Iranian influence as so many Americans like to claim. One reason Saddam invaded Iran in 1980 was the worry about the growing and dangerous influence of revolutionary Iran among Iraq's Shia population.
What America's defeat of Saddam did was replace the anti-American and anti-Iranian Iraqi government with a pro-American but less hostile to fellow Shia Iran government that fights terrorists as our ally rather than supporting terrorists who like to kill us.
This change that was positive for America left room for Iran to expand influence in Iraq, but only because we did not manage to support the new pro-American government and couldn't get Arab states to focus on supporting the Arab side of Shia-Arab Iraqis against Shia Persians rather than worry about the Shia side allying with the non-Arab Shia Persians.
The recent problem of Iran backing the PMF Shia militias was caused by the opportunity that the rise of ISIL gave Iran--which was enabled by the withdrawal of American troops form Iraq in 2011.
President Obama to his credit did order Iraq War 2.0 to reverse that self-inflicted wound. Although the war seemed designed to be slow enough to allow Obama's term to end before needing to confront their nuclear deal "partner" Iran post-ISIL caliphate while "doing something" to avoid blame for defeat.
And now we face the problem of reversing the expanded revolutionary Iranian influence in Iraq (and the entire region). Not that this will solve all the problems. But it sure will help.