Eta Sigma Phi is the national honorary collegiate society for students of Latin and/or Greek. Members are elected by local chapters which have been chartered by the society. The purposes of the Society, in the words of the Constitution, are "to develop and promote interest in classical study among the students of colleges and universities; to promote closer fraternal relationship among students who are interested in classical study, including inter-campus relationship; to engage generally in an effort to stimulate interest in classical study, and in the history, art, and literature of ancient Greece and Rome.
Eta Sigma Phi became a national organization in 1924, initiated by Classics students at the University of Chicago and Northwestern University. The Alpha Gamma Chapter at SMU was established in the early 1930's. Initiation of new members takes place in February. Criteria for membership include academic performance in the Latin/Greek course and teacher recommendation. Eta Sigma Phi is closely associated with the SMU Classical Studies Club, and members participate in joint activities.