Witnesses described scenes of terror and panic last evening as the attackers began shooting indiscriminately and then blew themselves up at the entrance to Ataturk airport, one of Europe's busiest hubs.
The assault, which comes at the start of Turkey's crucial tourist season, was the latest in a wave of attacks in Istanbul and the capital Ankara blamed either on Islamic State (IS) jihadists or Kurdish rebels.
There was no immediate claim of responsibility but Prime Minister Binali Yildirim said "the evidence points to Daesh", using another name for IS.
The dead include several Saudis, a Chinese national, a Tunisian and a Ukrainian.
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The carnage sparked global condemnation, with US President Barack Obama speaking by phone with his counterpart Recep Tayyip Erdogan to express his condolences, according to Turkish presidential sources.
Erdogan declared today a national day of mourning after urging an international "joint fight" against terror.
Security camera footage widely circulated on social media appeared to capture two of the blasts. In one clip a huge ball of flame erupts at an entrance to the terminal building, scattering terrified passengers.
The attack came just as Turkey, which had found itself increasingly friendless on the international stage, begins rebuilding relations with Israel and Russia.
It also follows coordinated IS suicide bombings at Brussels airport and a city metro station in March that left 32 people dead.
Women sobbed outside a local morgue, while families were desperately waiting for news of loved ones outside several Istanbul hospitals.
"Let me see him, I beg you," a woman screamed outside one hospital. "No one's told me what's happened to my child. I raised him. They're not telling me anything.