The Erasmus Programme, together with a number of other independent programmes, was incorporated into the Socrates programme established by the European Commission in 1994. The Socrates programme ended on 31 December 1999 and was replaced with the Socrates II programme on 24 January 2000, which in turn was replaced by the Lifelong Learning Programme 2007–2013 on 1 January 2007.

The programme is named after the Dutch philosopher Desiderius Erasmus of Rotterdam, known as an opponent of dogmatism, who lived and worked in many places in Europe to expand his knowledge and gain new insights, and who left his fortune to the University of Basel in Switzerland.At the same time, ERASMUS is a backronym meaning European Region Action Scheme for the Mobility of University Students.

By the time the Erasmus Programme was adopted in June 1987, the European Commission had been supporting pilot student exchanges for 6 years. It proposed the original Erasmus Programme in early 1986, but reaction from the then Member States varied: those with substantial exchange programmes of their own (essentially France, Germany and the United Kingdom) were broadly hostile; the remaining countries were broadly in favour. Exchanges between the Member States and the European Commission deteriorated, and the latter withdrew the proposal in early 1987 to protest against the inadequacy of the triennial budget proposed by some Member States.

There are currently more than 4,000 higher institutions participating in Erasmus across the 33 countries involved in the Erasmus programme and by 2013, 3 million students had taken part since the programme’s inception in 1987. In 2012-13 alone, 270,000 took part, the most popular destinations being Spain, Germany, and France.Erasmus students represented 5 percent of European graduates as of 2012.

A number of studies have raised issues related to the selection into the programme and the representativeness of the participants. Such studies have raised doubts about the inclusiveness of the programme, by socio-economic background, level of study, or academic performance. Thus, one study analyses the financial issues and family background of Erasmus students, showing that despite the fact that access to the programme has been moderately widened, there are still important socio-economic barriers to participation in the programme.Other study argues that the reason why the Erasmus programme misses its mark to reinforce a European identity is that it addresses university students, who are already very likely to feel European.Finally, a study finds out what seems to be an adverse self-selection of Erasmus students based on their prior academic performance, with higher-performing students less likely to participate than lower-performing ones.