Because these ruling families of Syria mostly hailed from Greece, they are variously called both "Syrian" and "Greek." This is why the Maccabean victory over Antiochus IV — celebrated to this day by the Jewish holiday of Hanukkah — is variously called a victory against the Syrians and a victory against the Greeks.
Antiochus IV was the first of two Greek rulers of Syria to escape Roman captivity before ascending to the throne.
Antiochus the Mad's son took the name Antiochus Eupater, which means "of a good father."
People named Antiochus, along with people named Seleucus, were the primary leaders of post-Alexandrian Syria. The successive Antiochuses are as follows, though details about the II, V, and VI are uncertain.
Antiochus II Theos ("God"), the younger son of Antiochus I, took over ruling the fledgling Seleucid dynasty in Syria after the death of his father. (Antiochus I's older son, Seleucus, was unable to inherit the kingdom because his father had killed him.)
Antiochus III Megas ("the Great"), born to Seleucus II, is known for capturing Jerusalem and making it a Syrian province. This was part of his more general campaign of expansion, which included a secret pact with Philip V (in Macedonia) to divvy up the territory controlled by the Ptolemies. Largely successful, he gave his daughter, Cleopatra I, to Ptolemy V in marriage, cementing his ties with Egypt. His fortune turned, though, particularly after Hannibal helped convince him to wage war on Rome. He lost that war, surrendering his son, Antiochus IV, as a prisoner.
Antiochus IV Epiphanes, often called Antiochus "the Mad," was born to Antiochus III, but early in his life, his father sent him to Rome as a hostage. Antiochus IV's brother, the ruling Seleucus IV, freed him by offering his (Seleucus's) own son Demetrius in exchange.
Antiochus IV is best known for his attempts to impose Hellenism across his Syrian kingdom. As part of that effort, he suppressed Judaism in Jerusalem, and even usurped control of the great Jewish Temple there, shifting its focus away from the God of the Jews and dedicating the Temple to the Greek god Zeus. This step provoked the Wars of the Maccabees, as marked by the Jewish holiday of Hanukkah and as described in the books of Maccabees.
Antiochus V Eupater ("of a good father") took over the Syrian empire after his father, Antiochus IV ("the Mad"), was killed in battle, but he didn't rule for long. His brother, Demetrius, who had been a Roman hostage, managed to escape, to return to Syria, and to seize control.
Antiochus VI Dionysus was born to Alexander Balas and Cleopatra Thea. Demetrius II Nicator killed Antiochus VI's father (perhaps because Antiochus VI's father had killed Demetrius II's father, Demetrius I). Because Alexander Balas was not actually part of the blood-line of Syrian rulers (though he pretended to be), Antiochus VI ruled in name only. Demetrius II, the legitimate heir of the ruling line, was the actual monarch during Antiochus VI's life.
Antiochus VII Sidetes — whose father was Demetrius I, and whose brother, therefore, was Demetrius II — is known for his close alliance with John Hyrcanus, the Jewish leader of Jerusalem whose vicious expansionist policies inadvertently paved the way for Jerusalem's suffering under Herod the Great. Antiochus VII tried to re-enlarge the failing Syrian empire by driving the Parthians from Mesopotamia. The Parthians surprised him with a counter-attack in 129 BC, during which he lost his life, and Syria, cast into civil war, lost any hope of regaining its former glory.