The migrant crisis is putting pressure on the Schengen Agreement, which abolished the EU's internal borders, enabling passport-free movement across most of the bloc.
Germany has brought back border controls, and several other countries are taking similar measures, all allowed under the accord but only temporarily and in exceptional circumstances
Only six of the 28 EU member states are outside the Schengen zone - Bulgaria, Croatia, Cyprus, Ireland, Romania and the UK.
Non-EU nationals who have a Schengen visa generally do not have ID checks once they are travelling inside the zone.
Schengen is a town in Luxembourg where the agreement was signed in 1985.
There are 26 countries in Schengen - 22 EU members and four non-EU. Those four are: Iceland and Norway (since 2001), Switzerland (since 2008) and Liechtenstein (since 2011).
Schengen took effect in 1995, the first members being: Belgium, France, Germany, Luxembourg, the Netherlands, Portugal and Spain.
They were followed by Italy and Austria in 1997, Greece in 2000, and the Nordic countries in 2001.
Nine more EU countries joined in 2007, after the EU's eastward enlargement in 2004. They are: the Czech Republic, Estonia, Hungary, Lithuania, Latvia, Malta, Poland, Slovakia and Slovenia.
Andorra and San Marino are not part of Schengen, but they no longer have checks at their borders.
There is no date yet for Cyprus, which joined the EU in 2004, or for Bulgaria and Romania, which joined in 2007.
The UK and Republic of Ireland have opted out. The UK wants to maintain its own borders, and Dublin prefers to preserve its free movement arrangement with the UK - called the Common Travel Area - rather than join Schengen.
The UK and Ireland began taking part in some aspects of the Schengen agreement, such as the Schengen Information System (SIS), from 2000 and 2002 respectively.
The SIS enables police forces across Europe to share data on law enforcement. It includes data on stolen cars, court proceedings and missing persons.
Germany has re-imposed controls on its border with Austria, after a record number of migrants travelled to southern Germany from Hungary, via Austria.
The influx of migrants - most of them fleeing Syria and other conflict zones - also pushed Austria to restrict road and rail traffic on its border with Hungary.
Slovakia is boosting controls on its borders with Austria and Hungary. The Dutch are introducing spot checks and Poland is also considering action.
The migrants entered the EU illegally, without Schengen visas. Hungary became a hotspot as a central gateway to the Schengen zone.
In June there was tension over Schengen when France prevented migrants - mostly Africans - entering from Italy, leaving them stranded at Ventimiglia train station.
In his State of the Union speech on 9 September the EU Commission President, Jean-Claude Juncker, called free movement under Schengen "a unique symbol of European integration".
The current crisis, he said, demanded "better joint management of our external borders and more solidarity in coping" with the influx.
Schengen has drawn intense criticism from nationalists and Eurosceptics EU-wide, such as the French National Front (FN), Dutch Freedom Party (PVV) and UK Independence Party.
Under the Schengen rules, signatories may re-instate internal border controls for 10 days, if this is necessary for "public policy or national security" reasons. If the problem continues, the controls can be maintained for "renewable periods" of up to 20 days and for a maximum of two months.
The foiled terror attack on a train in northern France in August fuelled anxiety about Schengen. It raised the question: how did a heavily-armed man manage to board an Amsterdam-Paris train in Brussels?
An EU regulation in 2013 specified that such controls "should remain an exception and should only be effected as a measure of last resort, for a strictly limited scope and period of time".
Any state that does so has to notify EU institutions and allow EU monitoring of the controls.
Besides the current crisis, France re-imposed border controls after the bomb attacks on London in 2005.
Austria, Portugal and Germany re-imposed border controls for some major sporting events, such as the Fifa World Cup.
Image copyrightReutersImage caption German police are now routinely checking vehicles entering from AustriaThe main feature is the creation of a single external border, and a single set of rules for policing the border. Among the other measures are:
Common rules on asylum;
Hot pursuit - police have the right to chase suspected criminals across borders;
Separation in airports of people travelling within the Schengen area from other passengers;
Common list of countries whose nationals require visas;
Creation of the Schengen Information System (SIS), which allows police stations and consulates to access a shared database of wanted or undesirable people and stolen objects;
Joint efforts to fight drug-related crime.
A Schengen visa is necessary to travel to a Schengen country or within the area. It is a short-stay visa valid for 90 days. It also allows international transit at airports in Schengen countries.
A short-stay visa costs €60 (£44; $68).
But the visa costs €35 for Russians, Ukrainians and citizens of some other countries, under visa facilitation agreements.
The EU has no visa requirement for citizens of Albania, Bosnia-Herzegovina, Macedonia, Montenegro and Serbia who have biometric passports. These Balkan nations all hope to join the EU. Kosovo is excluded from the arrangement.
Since the scrapping of visas for travellers from the Western Balkans there has been a surge in asylum applications from that region. Many asylum seekers are Roma (Gypsies), who are often desperately poor, marginalised and victims of discrimination.
Most of the asylum claims are submitted in Germany, which already has well-established diaspora communities from the Balkans.
An EU report says "asylum abuse has continued to afflict the visa-free scheme" and the situation "remains untenable". It calls for more aid for minorities, especially the Roma, in the Balkans, and much tighter co-operation between border authorities.
Now the EU is considering having a common list of "safe countries of origin", including the Western Balkans and Turkey. It would help speed up the processing of asylum claims, and give a legal basis for sending many Balkan applicants home. Fewer than 10% of applicants from the region get asylum in the EU.