Security was tightened across the jittery continent and transport links paralysed after the bombings that Belgian Prime Minister Charles Michel branded "blind, violent and cowardly".
"This is a day of tragedy, a black day," Michel said on national television.
Two blasts targeted the main hall of Zaventem Airport at around 8:00am (1130 IST), with prosecutor Frederic Van Leeuw saying the assault likely involved at least one suicide bomber.
A third hit Maalbeek metro station near the European Union's main buildings, just as commuters were making their way to work in rush hour.
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Witnesses said victims lay in pools of blood at the airport, their limbs blown off. There were chaotic scenes as passengers fled in panic, with a thick plume of smoke rising from the main terminal building.
"A man shouted a few words in Arabic and then I heard a huge blast," airport baggage security officer Alphonse Lyoura told AFP, his hands bloodied.
The explosions triggered a transport shutdown in the city that is home to the headquarters of both the EU and NATO. Flights were halted with metro, tram and bus services all suspended.
The bloodshed comes days after the dramatic arrest in Brussels on Friday of Salah Abdeslam -- the prime suspect in the Paris terror attacks claimed by the Islamic State group -- after four months on the run.
European leaders reacted with shock and solidarity, urging cooperation in the fight against terrorism on a continent that has been on high alert for months.
boosting security, including in London, Paris, Frankfurt and Amsterdam.
Major international train lines into Brussels were suspended, while security was also beefed up at Belgium's nuclear plants and at EU buildings in the French city of Strasbourg, home to the European Parliament.
Interior Minister Jan Jambon announced that Belgium's terror threat had been raised from three to a maximum of four, and the country's national security council was due to meet.
Residents were told to "stay where you are", while Deputy Prime Minister Alexander De Croo urged people to avoid making calls to stop the city's mobile networks getting saturated, and to communicate with online messages instead.
British premier David Cameron tweeted that his country would do "everything we can to help," and announced that Britain's COBRA security committee would meet today.
Russian President Vladimir Putin said the blasts "show once more that terrorism knows no borders and threatens people all over the world", according to a Kremlin statement.
"The fight against this evil requires vital international cooperation," he added.
The blasts come as Abdeslam, Europe's most wanted man, remains in a high-security prison in Belgium following his arrest last week in the gritty Brussels neighbourhood of Molenbeek, just around the corner from his family home.
At the airport, shaken witnesses spoke of how the blasts sent ceiling tiles shattering to the floor and left a smell of gunpowder in the air.
"We heard the explosion and felt the blowback," Jean-Pierre Lebeau, a French passenger who had just arrived from Geneva, told AFP, adding that he had seen wounded people and "blood in the elevator".
Jean-Pierre Herman and his wife Tankrat Paui Tran embraced with shock on their faces.
"When we came out of the elevator at that moment the second bomb exploded and then we saw doors flying, (the) glass ceiling come down and smoke."
At Maalbeek station, more than a dozen people with bloodied faces were treated by emergency services on the pavement, an AFP reporter said.