There are conflicting reports that between two and four bombers opened fire before blowing themselves up at several locations around Istanbul's Ataturk airport, Europe's third busiest.
Local news agencies are reporting Turkish police believe the self-proclaimed Islamic State are behind the attack.
There was mayhem at Istanbul's international airport.
Dozens have been killed and hundreds more wounded after bomb attacks at the city's Ataturk airport.
Turkish Prime Minister Binali Yildirim says three suicide bombers carried out the attack at the airport, before blowing themselves up.
"Officials are investigating this attack. So far, 36 victims have died and plus three suicide bombers died in this attack. There are large number of injured and some of them are in a serious condition."
Officials say police fired shots to try to stop the attackers just before they reached a security checkpoint at the arrivals hall of the airport but they blew themselves up.
One witness has told broadcaster NBC that a police officer had wrestled one of the attackers to the ground before he detonated his bomb.
Another witness has described the carnage.
"When I was in there, people were shooting on one side and we all ran the other way, and then the bombs went off. People started running the other way and there was more shooting, and we came out and after that I think there was another bomb, but not really sure. The wounded had cuts and people were very badly injured. One guy had holes in his back from shrapnel, from glass."
A traveller who witnessed the attack, Ali Tekin, said he heard two explosions.
"A big blast happened. It was very big and inside of it (the airport) is very bad. They also said there was gunfire, but I didn't hear. One person shot and injured. And there was two explosions. I heard the sound. I was inside the domestic terminal. It happened to those who were in international terminal."
Swedish Broadcasting Corporation Middle East correspondent Katja Magnusson was at the airport in the aftermath of the attack.
She told SBS the airport is closed and police investigators inside.
"I've been speaking to some of the people who were inside the airport and felt the explosion and also saw the blood and the damage that was caused after the explosion. A lot of people are quite shocked and a lot of people are still coming out from the airport - both airline staff and people who have been working in the airport and travellers."
Officials say the vast majority of the victims were Turkish nationals but foreigners were also among the casualties.
There was no immediate claim of responsibility for the attack, however Turkish authorities believe the self-proclaimed Islamic State are behind the blasts.
Turkish President Recep Tayyip Erdogan has strongly condemned the attack.
In a statement, he said the attack was aimed at undermining Turkey.
"It is clear that this attack is not aimed at achieving any result but only to create propaganda material against our country using simply the blood and pain of innocent people."
President Erdogan said he expected the world to show a decisive stance against terrorist groups following the attack.
Prime Minister Yilidrim says unity will be the best answer to these attacks.
"To unite, and this unity will the best answer, best reply to terrorists and terrorist attacks. Once again, I pray for mercy on the souls who lost their lives in this cowardly attack and pray, wish for a quick recovery for the injured ones. My condolences to all of our nation."
A Turkish Airlines official says authorities halted the take-off of scheduled flights from the airport and passengers were transferred to hotels.
Earlier an airport official said some flights to the airport had been diverted.
BBC journalist Mark Lowen was onboard a plane that landed at the airport shortly after the attack.
He has told the broadcaster that passengers were not advised of the situation on the ground before landing, and that their plane has been taken to a hangar where they are waiting to disembark.
"There's a fairly calm atmosphere here on the plane here, no sense of panic here at the moment. And the feeling that we could be here for a couple of hours. That is what we are being told by the cabin crew before we are allowed to disembark. But at the moment we are getting dribs or drabs of information from inside the airport."
Turkey has suffered a spate of bombings this year, including two suicide attacks in tourist areas of Istanbul blamed on IS, and two car bombings in the capital, Ankara, which were claimed by a Kurdish militant group.
Turkey is part of the US-led coalition against IS, but is also fighting Kurdish militants in its largely Kurdish southeast.
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