The explosions are believed to have happened in the departure lounge at the airport at around 8am UK time.
Police have confirmed at least one person have been killed and several injured.
Amateur video footage showed people running from the scene of the blasts.
Photos of the scene show damage to the terminal and windows blown out.
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UPDATE 8.26am: Belgian media reporting explosion at Brussels metro station.
UPDATE 8.54am: At least 13 people killed and 35 injured according to Belgian media reports.