The society was named after Dante Alighieri (1265–1321), a pre-Renaissance poet from Florence and the author of The Divine Comedy.

In July 2019 at the International Congress in Buenos Aires, the Società Dante Alighieri adopted a new statute stating that “the foreign committees are subject to the regulations dictated by their own legislation” and that in each committee’s “Constitution must be clear reference to the inspiring principles of the Società Dante Alighieri, the sharing of its aims and objectives and the need to sign the Convenzione di Affiliazione that governs the relationship between the Società Dante Alighieri and the committees.” The sole purpose of the Dante Alighieri Society is to "promote the study of the Italian language and culture throughout the world... a purpose independent of political ideologies, national or ethnic origins or religious beliefs, and that the Society is the free association of people – not just Italians – but all people everywhere who are united by their love for the Italian languages and culture and the spirit of universal humanism that these represent."

The society operates throughout the world, with branches from the United States to Australia.

Some of them are recognized as Centro d'esame autorizzato PLIDA - the Italian Certification Exam offered by Società Dante Alighieri.

In 2005, the Dante Alighieri Society (along with the Alliance française, British Council, Goethe-Institut, Instituto Cervantes, and Instituto Camões) was awarded the Prince of Asturias Award for Communications and Humanities.