Here are six facts and figures that will help explain the scale of the problem — and the challenges to solving it.
1. 340,000 migrants arrived in the EU in the first seven months of 2015
This is why it has been described as the worst migrant crisis since World War II: Nearly 340,000 migrants entered the European Union between January and July, according to the European Union's border control agency Frontex.
That compares with 123,500 for the same period in 2014 and 280,000 in all of last year.
In July alone a record 107,500 migrants were detected, more than triple the number for the same month last year.
"Syrians and Afghans accounted for a lion's share of the record number of migrants entering the EU illegally," Frontex said.
"Most of them, fleeing instability in their home countries, initially entered Greece from Turkey."
2. The EU received 184,800 asylum applications in the first quarter of 2015
European immigration officials have been inundated with applications for asylum.
In the first three months of this year a total of 184,800 people requested asylum for the first time, up a staggering 86 percent on the same period last year, according to Eurostat.
The top three nationalities seeking asylum were Kosovars (48,900), Syrians (29,100), and Afghans (12,900).
Authorities are struggling to keep up. Nearly 122,000 decisions were made, of which 46 percent resulted in "a type of protection status."
3. 267,121 migrants have crossed the Mediterranean Sea to Europe so far this year
One of the most popular routes into Europe is the Mediterranean Sea. So far this year, an estimated 267,121 people have made the perilous journey from North Africa and the Middle East, according to the International Organization for Migration.
Tens of thousands of them only survived after being plucked from the ocean by rescuers patrolling the waters.
On a recent Saturday, Italy's coast guard rescued more than 4,000 migrants off the coast of Libya after receiving distress calls from more than 20 boats.
4. 2,373 migrants have died attempting to cross the Mediterranean Sea so far this year
The tragic fact is many migrants don't survive the journey.
So far this year, 2,373 people — men, women, and children — have died attempting to cross the Mediterranean Sea in overcrowded and unseaworthy boats, the IOM said.
That makes it the deadliest migratory route in the world, accounting for 72 percent of the 3,279 migrant deaths worldwide this year.
Many migrants die before they make it to Europe and, as the gruesome discovery of dozens of bodies in an abandoned truck in Austria shows, even after they have crossed the border.
5. Five countries have received 80 percent of asylum applications
There might be 28 countries in the European Union, but just five — Germany, Hungary, Italy, France, and Sweden — took 80 percent of the asylum applications in the first three months of the year, Eurostat data shows.
Germany is taking the lion's share. German officials have said they expect to receive 800,000 asylum applications this year — nearly double the forecast made earlier this year.
That's more than any other EU country and way more than the 626,000 applications received by the entire EU last year.
Germany insists it can cope with the huge numbers of migrants, but it has called for a "fairer distribution" to ease pressure on the countries receiving most of them.
"This is a challenge for all of us, [but] Germany is not overwhelmed," Interior Minister Thomas de Maiziere told the BBC.
6. Double the attacks: Violence against migrants is on the rise
The influx of migrants is fueling tensions along national borders and has sparked violence and protests in towns where migrants are being housed in tents, gymnasiums, and disused hotels.
That is about twice the number during the same period in 2014.
There have also been protests as a small but vocal minority expresses their disapproval at the arrival of so many migrants.
But German Chancellor Angela Merkel said there would be "no tolerance" for anti-migrant violence.
Elsewhere in Europe, there have been disturbing scenes along Macedonia's southern border with Greece, where security forces have reportedly used stun grenades, tear gas, and rubber bullets to stop people from entering the country.
"These are very serious allegations of excessive force by the Macedonian police firing at people seeking protection," said Emina Cerimovic, research fellow at Human Rights Watch.
"Macedonian authorities should be protecting migrants, including children and those among them who may be fleeing war and persecution, not giving the police a green light to fire at them."
Hungary, which is constructing a razor wire fence along its border with Serbia to stop the flow of migrants taking the increasingly popular Balkans route into the EU, is also considering deploying the army.
That would be in addition to the thousands of police it has already sent to the area.