As supporters of an Iranian-backed militia stormed the U.S. Embassy in Baghdad on Tuesday, three influential men were notably in the crowd. They lead groups that are among Iran’s most powerful allies in Iraq. And they’ve shaken up U.S.-Iraqi relations many times before. Here’s what you need to know.

Jamal Jaafar Ibrahimi

Jamal Jaafar Ibrahimi, who goes by the nickname Abu Mahdi al-Muhandis, founded the Shiite militia that is at the center of the current drama: Kataib Hezbollah. After the U.S. strike on his brigade on Sunday, he’s the one who threatened U.S. forces that there would be a response.

But Muhandis is also now deputy head of the Popular Mobilization Forces (PMF), in Arabic called Hashd al-Shaabi, which is an umbrella organization uniting primarily Iran-backed Shiite paramilitary groups. The PMF was founded in 2014 after the prominent Shiite cleric Ayatollah Sistani issued a call for groups to help the Iraqi government fight against the Islamic State.

After the Islamic State was kicked out, however, media reports and rights groups have documented alleged abuses by PMF in newly liberated Sunni villages and neighborhoods. The revenge violence has allegedly included the looting of homes and the disappearance of male residents. Experts have warned that these kinds of sectarian crimes could fuel resentment ripe for the Islamic State’s resurgence.

In 2019, the Iraqi government officially integrated the PMF into Iraq’s armed forces. But there’s little oversight, as it reports to the Iraqi president rather than the Ministry of Defense. The around 50 paramilitary groups in the force also have competing political interests and alliances.

“Until the territorial defeat of ISIS, the Iraqi government needed the PMF and allowed their operational independence,” explained Philippe Atallah at the Philadelphia-based Foreign Policy Research Institute. “Now, without a common enemy, these militias have no explicit purpose, yet most refuse to disband and relinquish control over areas they control. The future of these militias is unclear, and the Iraqi government needs to take control of them or risk losing authority to militia leaders who act as Iranian proxies and regional warlords with personal armies.”

PMF supporters are the ones taking part in Tuesdays protests. It’s a very different crowd from the largely young, anti-Iran, anti-Iraqi government and all-around anti-establishment protesters who’ve been demonstrating in Baghdad and across Iraq since October. This second group of protesters are fed up with the post-2003 sectarian political system set up in Iraq, from which the militias benefit.

Kataib Hezbollah

The group stands for the Hezbollah, or party of God, brigade. It’s one of the smallest of the Iranian-backed militias in Iraq, but also one of the most powerful ones: While Iraq’s pro-Iran militias have varying degrees of proximity to Tehran, Kataib Hezbollah is one that’s reportedly quite close.

Muhandis, whose father was Iraqi and mother Iranian, formed the group in 2003 in the fallout of the U.S.-led invasion of Iraq. Some of the group’s estimated 5,000 members were among the first to go to Syria to fight for Iran’s ally, Syrian President Bashar al-Assad. They then took part in the battle against the Islamic State, briefly putting the group on the same side as its previous foe, the United States. To prepare, the brigade reportedly received battlefield training from Lebanon’s main Iran-backed militia, Hezbollah.

Muhandis also has a long rap sheet. He has been accused of helping to orchestrate the 1983 bombings in Kuwait of the United States and French embassies, in addition to four other sites. Five people died in the U.S. Embassy blast. In 2007, a Kuwaiti court sentenced an absentee Muhandis to death. That same year, the United States designated him a terrorist.

That hasn’t stopped him. Muhandis is now an adviser to one of Iran’s most powerful men: Qasem Soleimani, the commander of Iran’s Quds Force, a special arm of the Iranian Revolutionary Guard Corps that oversees Iran’s proxies abroad, among other missions.

Hadi al-Amiri

Also in attendance Tuesday was Hadi al-Amiri, a former transportation minister, who is considered Tehran’s man in Baghdad. Amiri heads the Badr Organization, which is one of the largest pro-Iran militias in Iraq and is part of the PMF. It was originally founded in the 1980s to fight for Iran against then-President Saddam Hussein as part of the Iran-Iraq war.

The Badr Organization fought U.S. forces after the invasion of Iraq in 2003 and in the brutal and bloody sectarian war that followed. Members have also gone to Syria to fight on Assad’s side. The group is additionally deeply embedded in Iraqi politics: The Badr Organization is the military wing of the Fatah coalition in Iraq’s parliament.

Qais al-Khazali

In December, the United States blacklisted the leaders of three militias in Iraq that it accused of opening fire on and killing peaceful anti-government protesters. Among them was Qais al-Khazali, who heads the Asaib Ahl al-Haq militia, one of Iraq’s most notorious pro-Iran militias that has launched numerous attacks against American and Iraqi forces since its founding in 2006.

U.S. forces arrested and imprisoned Khazali in 2007 for his alleged role in an attack that killed five U.S. soldiers. He was released in 2010 as part of a prisoner exchange.