Prime Minister David Cameron says he doesn't think letting more refugees into Britain is the best way of helping them.
But the photo of a dead toddler washed up on a beach seems to be changing some people's opinion on what should be done.
Britain's under increasing pressure to take its fair share of people in need but it sounds like Mr Cameron won't be budged.
So what is being done to help?
Warning: This article contains a distressing image further down the page
The UK says its aid donations are helping keep people alive
Hard cash
The government says it's spent £900m on aid to help people trying to escape the war in Syria.
Lots of that money has gone on helping the hundreds of thousands of people stuck in huge refugee camps along Syria's border, including Turkey, Lebanon and Jordan.
The cash is spent on basic things like running water, food, medicine and shelter.
The UK also spends billions of pounds every year on foreign aid - more than many other EU countries.
The number of people desperate to reach Europe has caused a crisis across the continent
Is giving money enough?
While Germany expects 800,000 asylum seekers this year, Britain doesn't want to sign up to any deal that forces it to accept more refugees.
Five thousand Syrians have been granted asylum in the UK in the past four years.
The BBC has chosen to publish only one photograph of Aylan Kurdi but others have chosen to show more graphic images
Only 216 people who are described as the most vulnerable refugees have been accepted in the past 12 months. Four million Syrians have fled their country.
There are calls from both the United Nations and senior British politicians for the UK to do more.
But, the government claims most people want to return to their homes one day - so it's better to spend money on the ground and look for political solutions rather than simply bringing people to live in the UK.
Thousands of people risk their lives trying to reach Europe
Who else is helping?
With European leaders unable to work out a solution to the problem, plenty of "normal" people are doing their bit.
Here are just a few examples from around the UK.
Several hundred pairs of wellies left at Glastonbury are being sent to people at the camps around Calais.
Marches are planned to show support for people coming to Britain.
Volunteers are driving vans packed with donated shoes, tents and other essentials to refugee camps.
Signing petitions demanding Britain take its "fair share" of people in desperate need.
So far, the government insists it won't change its policy on letting people into the country. But with pressure building at home and abroad, that could change.
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