The European Union has a number of relationships with foreign states. According to the European Union's official site, and a statement by Commissioner Günter Verheugen, the aim is to have a ring of countries, sharing EU's democratic ideals and joining them in further integration without necessarily becoming full member states.
EFTA and EEA
The European Free Trade Association (EFTA) was created to allow European countries to partake in a free trade area with less integration as within the European Communities (later European Union). Most of the countries initially in EFTA have since joined the EU itself, so only four remain outside, Norway, Iceland, Liechtenstein and Switzerland.
The European Economic Area (EEA) agreement allows Norway, Iceland and Liechtenstein to have access to the EU's internal market and vice versa. The four basic freedoms (goods, services, people, and capital) apply. However, some restrictions on fisheries and agriculture take place.
Norway
Norway is a member of the EEA, therefore it participates in the single market, and most EU laws are made part of Norwegian law. Norway has signed the Schengen treaty, which means border checks are no longer made.
Iceland
Like Norway, Iceland joined the EEA, and is considered part of the European Single Market. Iceland has also signed the Schengen treaty. In 2009 Iceland applied to join the Union but the application was controversial and the Icelandic government withdrew it in 2015.
Liechtenstein
Liechtenstein joined the EEA in 1995 and participates in the European Single Market.
Switzerland
The Swiss referendum to join the EEA in 1992 failed, so Swiss products do not participate in the European Single Market. However the country negotiated two series of bilateral agreements with the Union. The first series, Bilateral Agreements I, consists of seven bilateral agreements and was signed in 1999 (entry into force in 2001), the main part being Free Movement of Persons (full text of the agreement). The second series, Bilateral Agreements II, relates to nine areas and was signed in 2004 (entered into full force on 30 March 2005) and includes the Schengen treaty and the Dublin Convention (full text of the agreement) (official press release).
Eurozone-related
There are four European microstates which are neither EU member-states nor full eurozone members, but nevertheless use and mint the euro as their legal currency under official agreements with the EU. All of them previously used the national currencies of their larger neighbours, Italy, France and Spain, which have since all become eurozone-members.
: San Marino is not a member state of the EU, but had a special agreement with Italy to mint a limited number of its own lira coins. There is an agreement to mint its own euro coins (limited) which are legal tender in the eurozone. : The Vatican City is not part of the EU, but had a special agreement with Italy to mint a limited number of its own lira coins. There is an agreement to mint its own euro coins (limited) which are legal tender in the eurozone. : Monaco is not a member state of the EU, it had a special agreement with France to mint its own franc coins. There is an agreement to mint its own euro coins (limited), which are legal tender in the eurozone. : Andorra is not part of the EU. In the 20th century, both the French franc and Spanish peseta were used and accepted in Andorra, but the peseta was more widespread There is an agreement to mint its own euro coins (limited) which are legal tender in the eurozone.
In addition, two dependent territories outside of the EU use the euro as their currency under agreements with the EU, though without minting their own euro coins: is not a part of the EU, but there is an agreement with the EU to use euro as its currency, though without minting own euro coins. The French franc was used there before. is not a part of the EU, but there is an agreement between the United Kingdom and the EU to use euro as its currency, though without minting own euro coins. The Cypriot pound was used there before.
Some other countries unilaterally decided to use the euro as their de facto currency without having currently a formal agreement with the EU.