The Pentagon says more than a dozen missiles have been fired from Iranian territory.
The Ain al-Asad base in Anbar province and a base in Erbil have been hit.
Iranian state TV said the move was in retaliation to the assassination of General Qassem Soleimani.
US President Donald Trump has tweeted about the attack. He wrote, "All is well!" and said he'd be making a statement on Wednesday morning local time.
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