Pope Eleuterus lived during a time when some of the Christian churches were being persecuted, but this was not the case so much at Rome. Tertullian apparently refers to Eleuterus when he speaks of a Roman bishop who at first declined to condemn Montanism and later declared it to be heretical. This was an important moment in church history, for it brought to a close the earlier tradition of Christian prophecy and established the bishops as the final arbiters of orthodoxy in the Catholic tradition.
Eleuterus also issued an edict stipulating that Christians must not refuse to eat certain foods. It is not clear whether this was aimed at Jewish Christians, who refused to eat non-kosher foods; Gnostics, some of whom were vegetarians; or Montanists, who often fasted or ate a dry diet. In any case, the edict was a two-edged sword, correctly affirming that diet is unrelated to salvation, but unfortunately establishing a precedent that one could not be an observant Jew (or a vegetarian) and a Christian at the same time.
Ironically, the act for which Eleuterus was most famous—the conversion of the first Christian king in the British isles—is probably legendary.