So far it seems that there were no casualties. US military sources said troops were given enough warning to reach shelters before the missiles struck.
The attacks were Iran's response to the US killing last week of top Iranian General Qasem Soleimani in Baghdad. Iran has called that attack an "act of war" and "state terrorism" and vowed a response.
After the attacks, Iranian foreign minister Mohammad Javad Zarif tweeted in the early hours of Wednesday morning that Iran did not "seek escalation or war," saying the missile strikes were a proportion measure "in self defense under Article 51 of UN charter."
A top Iranian military commander has vowed a "stronger and more crushing" attack should the US respond with further strikes against Iran or Iranian forces in Iraq.
US President Donald Trump has not issued a formal statement or addressed the nation since the strike. On Twitter, he said that "All is well!"
"Missiles launched from Iran at two military bases located in Iraq," Trump added. "Assessment of casualties & damages taking place now. So far, so good! We have the most powerful and well equipped military anywhere in the world, by far! I will be making a statement tomorrow morning."
Flights have been diverted from Iraq, while multiple countries, including Japan, India and Pakistan have issued travel alerts urging citizens to avoid travel to the country. The Philippines issued its highest-level alert, urging the immediate repatriation of all citizens in Iraq.
All eyes are now on Washington, to see what Trump's response will be Wednesday morning.
2:40 a.m. ET, January 8, 2020
Iranian Armed Forces says if US retaliates, Iran's response "will be stronger and more crushing"
From CNN's Chandler Thorton
Iranian Armed Forces chief of staff Major General Mohammad Baqeri said that if the US retaliates against Iran after strikes against US forces in Iraq, Tehran's response "will be stronger and more crushing," according to the state-run news agency IRNA.
Baqeri's comments come after Iran launched more than a dozen ballistic missiles at two Iraqi military bases that house US troops Wednesday.
Addressing the operation against the bases, General Baqeri said "it was just a small part of the capabilities" of Iranian forces.
"Today, it is time for the wicked US officials to understand the Islamic Republic power and opt for a principled method to make its terrorist army leave the region."
1:42 a.m. ET, January 8, 2020
Philippines is latest country to order citizens to leave Iraq
From CNN's Carly Walsh and Joshua Berlinger
The Philippines has urged citizens in Iraq to leave the country, issuing the country's highest level of travel alert following Iranian missile strikes against bases housing US troops.
The alert calls for the mandatory repatriation of its citizens, but the Philippines presidential spokesperson Salvador Panelo said in an interview with CNN Philippines that while the government wants everyone to leave Iraq, it would be impossible to force Filipinos to do so.
CNN Philippines reports that military officials are considering "deploying C-130 planes and tapping the services of cruise ships" in order to carry out repatriation missions, while the country's Coast Guard is sailing a patrol vessel to Oman or Dubai.
The Philippine armed forces said in a tweet that there are 1,600 Filipinos in Iran and 6,000 in Iraq. Many work on oil rigs, in service industries and as domestic workers. If they evacuated and left their jobs, it could have a notable impact on the Philippine economy.
1:21 a.m. ET, January 8, 2020
The Fox factor: How Trump's favorite network could guide his Iran policy at a pivotal moment
Analysis from CNN's Oliver Darcy
When US President George W. Bush prepared to send troops into Iraq, there weren't a lot of questions about what TV networks or talk radio hosts were influencing his decisions. When his successor, Barack Obama, contemplated military action in Libya, Syria, and other countries, there weren't constant stories about what MSNBC hosts were advising him to do.
But as the US and Iran exchange military blows against each other in Iraq, it's not only possible, but perhaps likely, that what President Donald Trump sees on Fox News is shaping his views and guiding his decisions.
The situation is further compounded, of course, by the fact that the White House press secretary has stopped holding formal press briefings. Instead, to get a sense of what the President might be thinking, Americans are left with watching Fox News host Sean Hannity's show.
On Tuesday night, Lindsey Graham and Kevin McCarthy both appeared on his show, touting that they had spoken to Trump earlier.
Graham said Iran's fate was in its hands, warning, "You continue this crap you're going to wake up one day out of the oil business." And McCarthy praised Trump's judgement, telling Hannity, "He'll access the damage and he'll respond accordingly."
Japan has urged “all parties concerned to exhaust diplomatic efforts to ease tensions,” following Iran’s attack on military bases in Iraq housing US troops.
Speaking to reporters in Tokyo, Japan's Chief Cabinet Secretary Yoshihide Suga said the government is "deeply concerned over escalating tensions" in the Middle East, adding that "further escalation must be avoided."
He confirmed that the country's National Security Council met Wednesday to discuss the situation, including Prime Minister Shinzo Abe, the ministers of defense and foreign affairs.
Suga added that the government is currently deciding whether a planned trip by Abe to the Middle East will go ahead, but a plan to send a Self-Defense Forces ship and two aircraft to the region will remain on course for the time being.
That mission is aimed at gathering information to ensure the safe passage of Japanese commercial shipping through the Gulf of Oman, Gulf of Aden and the northern Arabian Sea.
A Japanese oil tanker was attacked in June this year in the Gulf of Oman.
1:06 a.m. ET, January 8, 2020
India urges citizens to "avoid all non-essential travel to Iraq"
From CNN's Swati Gupta in New Delhi and Sugam Pokharel in Atlanta
India's Ministry of External Affairs (MEA) has urged citizens to "avoid all non-essential travel to Iraq until further notification" in view of the "prevailing situation" following Iranian missile strikes against bases housing US troops in the country.
"Indian nationals residing in Iraq are advised to be alert and (should) avoid travel within Iraq," the MEA added in a statement.
"Our Embassy in Baghdad and Consulate in Erbil will continue to function normally to provide all services to Indians residing in Iraq."
Meanwhile, neighboring Pakistan urged citizens to "exercise maximum caution" while traveling to Iraq.
In a tweet, Pakistan’s Foreign Ministry spokesperson, Aisha Farooqui said that "in view of recent developments (and the) prevailing security situation in the region, Pakistani nationals are advised to exercise maximum caution while planning visit to Iraq at this point."
She also advised Pakistani citizens in Iraq to remain in close contact with Pakistan's embassy in Baghdad.
2:43 a.m. ET, January 8, 2020
Iran's strikes seem intended to avoid US deaths -- here's why that might be the case
Analysis from CNN's Nick Paton Walsh in Beirut, Lebanon
Iran's missile strikes against bases in Iraq housing US troops was not a response designed to kill the most Americans possible.
Iran will have known that in the early hours of the morning, US troops are normally asleep and the chances of inflicting casualties are lower.
Iran will also have known the US has a strong air defense that would likely have been on high alert. Tehran should have a grasp of how well its missiles would fare against such technology.
The missile attacks don't make sense if Tehran's goal was to really hurt US troops in large numbers -- like some had been pledging to do. They do make sense however as the execution of Supreme Leader Khamenei's order to strike back openly against US military targets in response to the killing of Iranian general Qasem Soleimani.
Khamenei's instruction was confusing when first reported, as the US is bound to prevail in a straight military-to-military conflict. Was the Supreme Leader ordering an empty show of force?
The dust is still settling, and even at the best of times Iran's motivations can be opaque, but there are three possible explanations for the action.
First, that Khamenei is out of touch with what his military can achieve and overestimated the effectiveness of the strikes, which then failed. This would be surprising given his reported involvement in and knowledge of Iranian military affairs.
Second, that moderation won out, and this largely empty signal -- hitting military targets in the dead of night with a small number of missiles -- provides the off-ramp both sides might ultimately want. This would be logical, given neither Tehran nor Washington have much to gain from a prolonged fight.
Third, this might be a bid by Iran to put the US into a false sense of security -- that Iran is militarily weak and has done its worse -- while an asymmetrical and nastier response is brewed. That would require a lot of strategic acumen from a government split between hardline and moderate wings, and means Tehran was relatively assured no Americans would be hurt in this missile attack.
If the attacks in Iraq are indeed the full scope of Iran's response, they carry with them another risk: that the Trump administration think their ramshackle performance over the last week has paid off, and Iran has been vanquished. This would risk further irrational action from Washington, perhaps not just against Iran but also other enemies. It also makes Iran look weak, which may embolden Tehran's other regional adversaries.
Iran's response to the killing of Soleimani was always going to be difficult to predict. But -- if the strikes truly are the entirety of Tehran's revenge -- few would have anticipated something so swift and so openly military-to-military.
12:53 a.m. ET, January 8, 2020
US troops were patrolling outside their bases after attack on al-Assad, military official says
From CNN's Ingrid Formanek in Baghdad
US troops were actively patrolling outside their bases with Iraqi partners in the hours after Iran targeted two military bases that house US troops in Iraq, according to a military official who did not want to be named.
Drones and attack helicopters were flying around bases housing US troops, the official said.