The European Commission has told staff to remain indoors or stay at home.
"EU institutions (are) working together to ensure security of staff and premises. Please stay home or inside buildings," said Budget Commissioner Kristalina Georgieva, who also handles employee and security issues, on her official Twitter account.
Illustrations of the location of the blasts at Brussels' Zaventem airport.
Latest: Brussels transport authority says it has closed all public transport in Brussels.
Latest: The explosions at Brussels' Zaventem airport were carried out by a suicide bomber, Belgian broadcaster VRT said.
Camera phone video shows passengers being evacuated from the terminals at Brussels' Zaventem airport and out onto the tarmac.
The scene outside the Maalbeek subway station, where a blast was reported.