Witnesses described deadly carnage and crowds in a panic as the attackers struck.
At least 36 people were killed, Turkish Prime Minister Binali Yildirim said, in the terror attack, one for which there was no immediate claim of responsibility.
Another 147 people were wounded, Turkey's Justice Minister Bekir Bozdag said.
Sue Savage was in the airport to see a friend off when she heard gunshots and then an explosion, which she knew was a bomb. Then more gunshots and another boom, she told "Erin Burnett OutFront."She ducked into a men's prayer room and then into a men's toilet, where she hid in a stall with a young woman. They came out, perhaps 20 or 30 minutes later, and heard more screams and gunshots and ducked into a room where luggage is inspected.
She and about 30 people were herded into a women's prayer room until authorities led them out and down an escalator into the main terminal hall.
"There was a lot of blood," she said. The floor was marked with bloody boot marks and she saw a woman's scarf on the floor. The group was herded around to the other side of the room.
"There was so much glass on the floor they were scuffing it aside so we didn't slip," she said.
Photos: Istanbul airport attacked
Video from inside the airport terminal shows people racing away as fast as they could and the bright orange flash of fire from one of the explosions. Victims stagger and some fall from the now blood-covered, slick floor.
Another video shows a man walking with a gun, which he drops when he apparently is shot by a security officer. The man slumps to the ground and the officer briefly stands over him before running. About 10 seconds later, there is an explosion.
Traveler Laurence Cameron described what he saw after he stepped off a plane.
"It was just a massive crowd of screaming people. Some were falling over themselves. A poor chap in a wheelchair was just left, and everyone just rushed to the back of the building, and then people ran the other way and no one really seemed to know what was going on," he told CNN. "Where you normally hail a taxi, that is where the attack happened. The ground is just kind of shredded. There are bloodstains on the floor as well."
Terrorist attack in Istanbul Ataturk airport