Seven countries, as well as Kosovo, are waiting in the wings to join the European Union.
Kosovo's independence is not recognised by all EU countries, but the EU nevertheless views it as a potential candidate for membership.
Croatia and Turkey started accession talks on 3 October 2005. Croatia joined on 1 July 2013. Turkey could complete negotiations in 10-15 years, but progress has been very slow, as the EU is divided over whether Turkey should join at all.
The other Balkan countries have been told they can join the EU one day, if they meet the criteria. These include democracy, the rule of law, a market economy and adherence to the EU's goals of political and economic union.
Applied for full membership: April 2009
Confirmed as candidate: June 2014
Albania is not expected to join the EU until 2020 at the earliest. It got candidate status in June 2014 - recognition of its progress in reforming institutions to meet EU standards.
But the EU urged Albania to do more to tackle corruption and organised crime, especially crime relating to immigration and human trafficking, and drugs.
Since 15 December 2010 Albanians with biometric passports have been able to travel visa-free to the Schengen zone, which includes most EU countries.
Border controls are minimal under the Schengen accord, but the EU will keep a close watch on the flow of visitors from the Western Balkans.
The EU and Albania concluded a Stabilisation and Association Agreement (SAA), seen as the first step towards membership, in June 2006.
The negotiations took three-and-a-half years - three times longer than they took in Croatia's and Macedonia's case.
Bosnia-Hercegovina has not yet formally applied for EU membership.
More than a decade after the 1992-5 war, it signed a Stabilisation and Association Agreement (SAA) with the EU in June 2008. The EU was satisfied with progress in four key areas - police reform, co-operation with the international war crimes tribunal, public broadcasting and public administration reform.
Visa-free travel to the Schengen zone began in mid-December 2010 for Bosnians with biometric passports.
But in February 2014 public grievances with local politicians and the country's economic stagnation exploded, with attacks on government buildings.
The EU maintains a peacekeeping force and a police mission in Bosnia-Hercegovina, where most Serbs live in the autonomous Republika Srpska. The Bosniak-Croat federation and Republika Srpska together form Bosnia-Hercegovina.
Bosnia's ethnic quarrels remain a worry for the EU, along with corruption and organised crime.
The Commission says Bosnia is still plagued by an "unstable political climate" and ethnic divisions.
In December 2011 Bosnia's Muslim, Croat and Serb leaders agreed on the formation of a central government, ending 14 months of political deadlock.
The European Court of Human Rights has ruled that Bosnia's electoral laws discriminate against Jews and Roma (Gypsies), because only Bosniaks, Croats and Serbs are allowed to run for high office.
Applied for full membership: February 2003
Negotiations started: October 2005
Joined EU: July 2013
Croatia is the second ex-Yugoslav country after Slovenia to join. It is also the first new EU member state since Bulgaria and Romania joined in 2007.
Croatia's accession was widely seen as a strong signal of EU commitment to a region that was ravaged by war in the 1990s. Some see it as a triumph for EU "soft power", salvaging the EU's reputation after Europe's failure to prevent atrocities in the Balkan wars.
Even after they had joined in 2007 Bulgaria and Romania fell short of EU standards, notably in their efforts to root out corruption and political interference. So the requirements for Croatia were particularly strict.
The welcome for Croatia was somewhat muted, as surveys suggested that "enlargement fatigue" and anxiety about migrant workers were widespread in Europe.
Judicial reform was among the toughest of the 33 negotiating areas, or "chapters". EU Justice Commissioner Viviane Reding said that "in one year they have completely reformed their judiciary system and have made it irreversible".
The highest-profile target in Croatia's crackdown on corruption was former Prime Minister Ivo Sanader. A Croatian court sentenced him to 10 years in prison for taking bribes, in November 2012. He had been arrested in Austria and extradited to Croatia. He denied wrongdoing.
He was convicted of taking millions of dollars in bribes from a Hungarian energy company and an Austrian bank.
Prime Minister Jadranka Kosor replaced four ministers in the government she inherited from Mr Sanader.
A European Commission report in March 2011 said Croatia must make appointments of judges and state prosecutors more transparent, clear court backlogs, pursue high-level corruption investigations more thoroughly and do more to help disadvantaged minorities.
A border dispute with neighbouring Slovenia - an EU member - held up Croatia's accession talks until early September 2009, when Slovenia agreed to lift its veto over the talks.
Back in 2005 accession talks were delayed by seven months as Croatia struggled to convince the EU it was doing its best to find war crimes suspect Gen Ante Gotovina. He was arrested in the Canary Islands in December 2005.
On 15 April 2011 the war crimes tribunal in The Hague sentenced Gen Gotovina and another wartime Croat general, Mladen Markac, to 24 and 18 years in jail, respectively. They were found guilty of atrocities against Serbs in 1995. There was widespread anger in Croatia over the sentences.
But on 16 November 2012 both generals were released after appeals judges overturned their sentences. They were greeted as heroes on their return to Zagreb.
Applied for full membership: July 2009
Negotiations started: July 2010
The EU has opened accession talks with Iceland. In October 2012 the EU Commission reported that 14 of the 33 areas of negotiation - called "chapters" - had been opened. Of those, eight have been provisionally closed - in other words, Iceland has met the criteria.
But there is now a big question mark over Iceland's bid to join.
A new centre-right coalition government took office in May 2013 and immediately announced that a referendum would be held on EU membership before any further accession negotiations.
Iceland's independence from continental Europe has provided fertile ground for Eurosceptics, and recent opinion polls suggest a strong "no" camp. The North Atlantic island, home to just 320,000 people, will not join unless Icelanders support it in a referendum.
Iceland is in dispute with the EU over mackerel fishing. Reykjavik objects to the EU and Norway taking more than 90% of the total allowable catch recommended by scientists. Iceland increased its 2011 quota unilaterally by nearly 17,000 tonnes.
Another sensitive area is financial reform, with Iceland still reeling from the collapse of its major banks in 2008.
In two referendums Icelanders have rejected compensation deals struck by their government with the UK and the Netherlands over savings lost by investors in the collapsed Icesave online bank.
The UK and Dutch governments want Iceland to reimburse the estimated 4bn euros (£3.4bn; $5.3bn) that they paid as compensation to Icesave investors.
According to Iceland's President, Olafur Ragnar Grimsson, assets from the collapsed bank Landsbanki will cover what is owed.
The European Commission says Iceland is already deeply integrated with the EU - it applies about two-thirds of EU laws - so it has less distance to cover than other applicants. But the EU is not offering any "shortcut".
Iceland is in the Schengen zone, meaning its people enjoy passport-free travel to many European countries. Iceland also applies many of the EU's single market rules.
The Icelandic krona has plummeted in value since the financial crash, but many Icelanders may still prefer to keep it. The fallout from Europe's debt crisis means the euro has lost some of its lustre.
Some Icelanders fear the impact of EU regulations on their traditional fisheries and whaling.
Icelandic membership would give the EU a more significant role in the Arctic - a region rich in untapped energy and mineral resources.
In the Balkans the breakaway territory of Kosovo is last in the queue to join the EU because the international community remains split over its 2008 declaration of independence.
The ethnic Albanian majority in Kosovo has been striving for international recognition since the 1999 conflict, in which Serb forces, accused of atrocities against civilians, pulled out after heavy Nato bombing.
Many countries have recognised Kosovo. But Serbia is among those that do not - a group that includes Russia, China and five of the 27 EU member states - Spain, Greece, Romania, Slovakia and Cyprus.
For more than a decade the hostility between Belgrade and the Kosovan authorities in Pristina has held up consideration of a Kosovan EU bid. Belgrade supports ethnic Serbs in northern Kosovo - about 50,000 people - who refuse to be governed by Pristina.
But a landmark Serbia-Kosovo deal, brokered by the EU on 19 April 2013 after months of arduous negotiations, paves the way for both Serbia and Kosovo to make progress towards EU accession.
Both sides pledged that they would not try to block each other's EU bid.
The deal grants a high degree of autonomy to the Serb-majority areas in Kosovo, and allows them their own ethnic Serb police chief and ethnic Serb appeal court.
EU governments will now open talks with Kosovo aimed at reaching a Stabilisation and Association Agreement - a first step towards EU membership.
The Commission also proposed allowing Kosovo to participate in 22 EU programmes.
In a report the Commission praised Pristina's co-operation with the EU law-and-order mission in Kosovo, called Eulex. It highlighted the smashing of a smuggling ring and other joint investigations into organised crime and corruption.
The report calls for further efforts to tackle human trafficking in Kosovo, and the gangs that smuggle drugs and illegal weapons.
Protection of minority rights and freedom of speech are also significant challenges that Kosovo must meet on the path to EU membership, the Commission says.
Applied for full membership: March 2004
Confirmed as candidate: December 2005
The European Commission has recommended that the EU open membership talks with Macedonia.
It says the former Yugoslav republic has made "convincing progress" in police reform, tackling corruption and bolstering human rights.
Since 19 December 2009 Macedonians have not needed visas to visit most EU member states - those in the Schengen zone.
Hopes that accession talks would open in 2008 suffered a blow from election violence in June and a subsequent boycott of parliament by ethnic Albanian opposition parties.
But the June 2011 parliamentary elections were "transparent and well-administered", EU governments said.
A bitter dispute with Greece over Macedonia's name continues to hamper the country's bids to join the EU and Nato.
Macedonia was admitted to the United Nations in 1993 using the temporary name of the Former Yugoslav Republic of Macedonia (Fyrom).
Greece argues that the name "Macedonia" cannot be monopolised by one country, and that doing so implies a territorial claim over the northern Greek region of the same name.
In a November 2008 interview, Macedonian Foreign Minister Antonio Milososki said "it is important that 125 countries worldwide have recognised Macedonia's constitutional name," and added: "we remain firm on our stance that only the Republic of Greece has a problem with Macedonia's constitutional name".
Applied for full membership: December 2008
Confirmed as candidate: December 2010
Negotiations started: June 2012
Candidate status has boosted Montenegro's bid and the EU opened the country's accession talks on 29 June 2012.
The EU says Montenegro must intensify its efforts to consolidate the rule of law, fight organised crime and corruption and protect freedom of expression.
Talks with the EU on a Stability and Association Agreement (SAA) began shortly after the country voted, in May 2006, to end its union with Serbia. The SAA was signed in October 2007.
Montenegro's Prime Minister, Milo Djukanovic, has said he hopes his country will succeed in joining the EU before neighbouring Serbia or Macedonia.
Since 19 December 2009, citizens of Montenegro have not needed visas to visit most EU countries - those in the Schengen zone.
Applied for full membership: December 2009
Confirmed as candidate: March 2012
Serbia's progress towards the EU has been sluggish - it is trailing far behind its neighbour Croatia, a bitter enemy in the 1990s Balkan wars.
But EU leaders granted Serbia candidate status at a Brussels summit in March 2012.
Then in June 2013 they decided that EU accession negotiations with Serbia would go ahead, after Belgrade had clinched a landmark deal with Kosovo, allowing for a normalisation of ties. The accession talks will begin by January 2014 at the latest, the EU says.
A Commission report said the leaders of Serbia and Kosovo had shown "political courage and maturity" in tackling difficult issues jointly, as well as a commitment to better relations.
Earlier Belgrade had agreed to allow Kosovo to take part in west Balkan regional meetings, despite refusing to recognise its independence. And the two sides agreed to control their volatile border jointly.
A UN resolution in September 2010, in which Serbia dropped its demand to reopen negotiations on Kosovo's status, signalled Belgrade's willingness to compromise.
Serbia's EU prospects improved after the arrest on 26 May 2011 of Europe's most wanted war crimes suspect, Gen Ratko Mladic. The former Bosnian Serb commander had been on the run for 16 years.
EU Enlargement Commissioner Stefan Fuele said "a great obstacle on the Serbian road to the European Union has been removed".
Serbia's co-operation with the international war crimes tribunal in The Hague remains a key condition in its accession bid.
In July 2011 the last major indictee wanted in The Hague, former Croatian Serb leader Goran Hadzic, was arrested in northern Serbia and sent to The Hague for trial.
The two figures blamed the most for Bosnian Serb wartime atrocities are now on trial in The Hague - Gen Mladic and Radovan Karadzic, who was arrested in Serbia in 2008.
Serbia is unlikely to join the EU until at least 2020.
Citizens of Serbia and two other former Yugoslav republics - Macedonia and Montenegro - enjoy visa-free travel to the Schengen area, which includes most of the EU. The visa waiver applies to those who hold biometric passports.
Serbia signed a Stabilisation and Association Agreement (SAA) with the EU in April 2008, but only in June 2010 did EU foreign ministers agree to put it into effect.
Applied for full membership: 1987
Confirmed as candidate: December 1999
Negotiations started: October 2005
Turkey met the last condition for accession talks in July 2005, when it extended a customs union with the EU to all new member states, including Cyprus.
However, it failed to ratify the customs union and its ports and airports remain closed to Cypriot traffic. The EU responded, in December 2006, by freezing accession talks in eight policy areas.
In May 2012 the EU and Turkey launched a highlighting areas where they could expand co-operation.
But Cyprus took up the EU's six-month rotating presidency in July 2012 and progress stalled, as Turkey refused to talk to the Cyprus authorities. Tensions remain over the breakaway ethnic Turkish administration in northern Cyprus, which is only recognised by Ankara.
So far only 13 of Turkey's 35 negotiating chapters have been opened, and only one has been closed.
The negotiations have been overshadowed by concerns about freedom of speech and democracy in Turkey, treatment of religious minorities, women's and children's rights, civilian control of the military and the Cyprus tensions.
Germany's Chancellor Angela Merkel was among many European politicians who condemned the conservative ruling AK Party's crackdown on mass street protests in June 2013. Tensions escalated into a diplomatic row between Germany and Turkey.
Police used tear gas and water cannon against demonstrators, who had initially staged a peaceful sit-in to stop a building project at Gezi Park, in the heart of Istanbul.
Some senior politicians in the EU - including Chancellor Merkel - want Turkey to have a partnership deal with the EU, rather than full membership.
Some politicians worry that such a large, mainly Muslim country would change the whole character of the EU, while others point to the young labour force that Turkey could provide for an ageing Europe.
The European Commission has urged Turkey to strengthen democracy and human rights, underlining the need for deeper judicial reform. The Commission's October 2012 report on Turkey criticised various human rights abuses, including the use of anti-terror laws to detain Kurdish rights activists and curb freedom of speech.
Turkey reacted angrily to that criticism, saying the EU had undervalued Ankara's reforms, instead displaying "biased" attitudes.
EU governments praised the "full respect of democratic standards and the rule of law" in Turkey's June 2011 parliamentary elections.
The EU also welcomed the Yes vote in a Turkish referendum in September 2010, which gave the AK Party the go-ahead to change the military-era constitution and bring it more into line with EU norms.
The UK Foreign Office says it expects Turkey to be ready for membership "in a decade or so".