There were two explosions in Zaventem Airport on the morning of March 22, followed by another at Maalbeek metro station.
Thirty-one people have died and many more have been hurt.
Three days of national mourning have been announced and a minute's silence has been observed.
Belgian Prime Minister Charles Michel said: "This is a day of tragedy, a black day... I would like to call on everyone to show calmness and solidarity."
Police and emergency services worked quickly to help those who were injured. All public transport in Brussels was shut down for much of the day.
Read this advice if you feel upset by the news.
Since the attacks, hundreds of messages of support for the people of Brussels have been chalked across the Place de la Bourse, a central square in the city.
As well as the chalk messages, which are written in many different languages of the world, flags have been displayed and flowers and candles left.
There's extra security at some airports to help keep people safe in the UK and other European countries.
British Prime Minister David Cameron has held a meeting to talk about how to keep the UK safe.
He said Britain would "do everything we can to help".
In November 2015 several attacks took place across Paris, the capital of France, in which 130 people died.
Some people think that these latest attacks may be linked to the Paris ones, but we don't know for sure.
The group that calls itself Islamic State has claimed responsibility - it also carried out the Paris attacks.
Last Saturday police in Belgium caught a man they think was involved in the Paris attacks.
They are now looking to see if what happened in Brussels is linked to that arrest.
US President Barack Obama has offered Belgium any help necessary in investigating the attacks.
It's important to remember that things like this are extremely rare - that is why they're in the news.
If you're feeling worried then it's best to talk to someone you trust, like a parent or teacher.
There's more advice here on if you're upset by the news.

The Barn Surgery in Christchurch was criticised by the Care Quality Commission (CQC) following an inspection in May last year.
A new inspection in February found the practice had made a "significant number of improvements".
The surgery is now rated "good" overall, the CQC said.
But it still "requires improvement" in the assessment category for "being effective".

Dame Sally Davies said the action by the British Medical Association (BMA) would "lead to patients suffering".
The strike begins across England at 08:00 GMT, from when junior doctors will only provide emergency care.
The BMA said the strikes "demonstrated the strength of feeling amongst the profession".
It announced three spells of strike action in England in November, after negotiations with the government ended without resolution.
Issues being disputed by the BMA and NHS include weekend pay.
"As a doctor, I can understand the anger and frustration felt by many junior doctors at this time," Dame Sally said.
"In part, this dispute is a symptom of frustration and low morale that has been building for decades and the strain that a career in medicine can place on your work-life balance.
"Junior doctors are the backbone of the NHS, working long and anti-social hours... It is vital that, as senior medical leaders, we ask ourselves whether we are doing everything we can to ensure our junior colleagues feel valued."
The planned strikes are set to take place from:
Conciliation service Acas has confirmed that talks between the BMA and NHS bosses will continue next week.
Junior doctors' leaders are objecting to the prospect of a new contract.
The government has described the current arrangements as "outdated" and "unfair", pointing out they were introduced in the 1990s.
Ministers drew up plans to change the contract in 2012, but talks broke down last year.
The government has indicated it will impose the new contract next year in England. The BMA has responded by initiating the industrial action process.
Junior doctors row: What you need to know
What exactly do junior doctors do?
There have been a number of attacks in the city of Brussels, the capital of Belgium.
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A GP surgery in Dorset that was rated inadequate after inspectors found staff shortages put patients at risk has been taken out of special measures.
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Junior doctors should suspend Tuesday's strike action over pay and conditions while talks continue, the chief medical officer for England has urged.