A firefighter told reporters that 11 people are dead and at least 20 people are injured.
A Belgian news agency also reported that witnesses had said they heard gunshots and shouts of Arabic at the time of the explosions fuelling fears that this may have been an attack inspired by islamic State (ISIS) terrorists.
An explosion has reportedly taken place at Maelbeek metro station in Brussels centre.
The large explosions have taken out glass windows at the entrance and much of the airport's ceiling has collapsed.
Other explosive devices have been discovered at the airport, firefighters have told journalists at the scene.
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