Two blasts tore through the departures area of Zaventem airport shortly after 08:00 local time (07:00 GMT).
An hour later, an explosion hit Maalbeek metro station, close to the EU institutions. The airport and whole transport system have been closed.
The attacks come four days after Salah Abdeslam, the main fugitive in the Paris attacks, was seized in Brussels.
The Belgian government has confirmed casualties at the airport but has given no numbers. The cause of the explosions is unknown.