The earliest Church Fathers, (within two generations of the Apostles of Christ) are usually called the Apostolic Fathers. Important Apostolic Fathers include Clement of Rome, Ignatius of Antioch and Polycarp of Smyrna. In addition, the Didache and Shepherd of Hermas are usually placed among the writings of the Apostolic Fathers although their authors are unknown; like the works of Clement, Ignatius and Polycarp, they were first written in Greek.
Those who wrote in Greek are called the Greek (Church) Fathers. Famous Greek Fathers include: Clement of Rome, Irenaeus of Lyons, Clement of Alexandria, Athanasius of Alexandria, John Chrysostom, Cyril of Alexandria the Cappadocian Fathers (Basil of Caesarea, Gregory Nazianzus, Peter of Sebaste & Gregory of Nyssa), Maximus the Confessor, and John of Damascus.
Those fathers who wrote in Latin are called the Latin (Church) Fathers. Famous Latin Fathers include Tertullian (who later in life converted to Montanism), Cyprian of Carthage, Gregory the Great, Augustine of Hippo, Ambrose of Milan, and Jerome.