It was founded in 1968 when its forerunner organisation the Communist League (Ligue Communite) was banned.
Its official spokesman is Alain Krivine, a member of the European Parliament, but Olivier Besancenot was the candidate for the 2002 French presidential election.
An ongoing issue is the possibility and conditions of an electoral alliance with fellow Trotskyist party Lutte Ouvrière. In the past the two have at times run joint candidates (for example in the last European elections), and at times run seperately (for example in the last presidential elections).
LCR militants openly work within left-wing groups such as ATTAC and the Solidaires Unitaires Démocratiques trade unions.
Although it still declares itself to be a Trotskyist group its recent Congress voted to abandon use of the term Dictatorship of the Proletariat to describe its political aims. It also includes members of other Trotskyist tendencies who are able to organise openly within its ranks to gain support for its views.