Summarizing US-Iran clashes since 2018

Nathaniel Davis provides a helpful summary of the clashes between the US and Iran since the US withdrawal from the nuclear arms-control treaty with Iran, The Rockets of January: Have We Really Escaped ‘A Trap From Which There Was no Exit’? Responsible Statecraft 01/14/2020:

Recent provocations included escalating attacks on U.S. forces in Iraq by Iranian-backed militias. Grown out of militias that fought against coalition forces during the Iraq War, they were reconstituted and rebranded with Iranian help to fight against ISIS. Modeled to some degree on Lebanese Hezbollah, they constitute a state within a state, and are part of the reason for months of protests in Baghdad against government corruption and Iranian influence in the country. These attacks culminated in a rocket attack near Kirkuk on December 27, in which a U.S. contractor was killed and several U.S. and Iraqi military personnel were wounded. The U.S. retaliated on December 29, striking five Kataeb Hezbollah bases in Iraq, killing at least 25. The militia responded by violently protesting at the U.S. embassy in Baghdad, causing extensive damage, including graffiti reading “Soleimani is my commander.” The U.S. answered by sending Marines to the embassy, deploying portions of the 82nd Airborne Division’s Immediate Response Force to the region, and targeting Soleimani.

Since the killing of Soleimani, Iranian state television called the act the “the biggest miscalculation by the U.S.” in the post-World War II period, a telling statement when one considers that same period includes the U.S.-backed coup of Mohammad Mosaddegh in 1953, U.S. support for the Shah of Iran through 1979, and the accidental downing of Iran Air Flight 655 by USS Vincennes in 1985, all cardinal sins in the eyes of the Iranian regime. Iranian Supreme Leader Ayatollah Ali Khamenei warned of “harsh retaliation,” and the U.S. Embassy urged Americans to leave Iraq immediately. The Iraqi parliament voted along sectarian lines on a non-binding resolution to expel U.S. forces, and President Trump responded with a threat of sanctions. On January 5, Iran announced that it would no longer abide by the restrictions of the nuclear agreement, opening the door to the development of a nuclear weapon as a hedge against the threat of regime change. On Wednesday, Iran launched multiple ballistic missiles at bases housing U.S. forces in Iraq. The visually spectacular attacks resulted in no casualties, and it is possible that the strikes were designed with that outcome in mind. Following the attacks, Iranian foreign minister Javad Zarif tweeted “Iran took & concluded appropriate measures…We do not seek escalation or war, but will defend ourselves against any aggression.” In remarks on January 9, President Trump made it clear that the U.S. response to the strikes would be increased economic sanctions, rather than a military response. For the moment at least, it appears that the chain of escalations emanating from the death of Soleimani has been broken by mutual acts of restraint by both the U.S. and Iran.

Davis stresses the restraint is not some permanent state of affairs. To back away from the escalatory spiral since Trump left the JCPOA nuclear agreement will require constructive measures to reduce the tension.

Another piece at Responsible Statecraft by Gary Sick looks at the actual common interests of the US and Iran, How the U.S. and Iran Can Work Together on Their ‘Shared Priorities’ 01/13/2020.
Suadad al-Salhy (Iran tasked Nasrallah with uniting Iraqi proxies after Soleimani's death 01/14/2020)

The leaders of Iranian-backed paramilitary groups in Iraq have agreed to put their differences aside and back Hadi al-Amiri as the new chairman of the Popular Mobilisation Forces (PMF) as part of a wider plan brokered by Hezbollah leader Hassan Nasrallah to quell tensions between the groups and create a “united resistance” to US troops in the country. ...

Most of the leaders then flew to Tehran on Sunday, before moving onto the Iranian city of Qom on Monday where they also met with influential Iraqi cleric Moqtada al-Sadr in a significant display of Shia unity.

Iraq is majority Shi'a. But that doesn't mean there aren't real tensions between Iraqi and Iranian Shi'a:

Iran is facing unprecedented tension in its relationship with the United States after it bombed Iraqi military bases hosting US forces last week, in retaliation for the killings of Soleimani and Muhandis.

In addition, the relationship between Sistani, the spiritual leader of the Shia community in Iraq, and [Iranian Ayatollah] Khamenei has deteriorated significantly because of the Iranian supreme leader's insistence on using Iraq as a proxy battleground for the confrontation with the US, and over the role of Iranian-backed armed groups in the killing and intimidation of Iraqi anti-government protesters.