Herod the Great reigned in Judæa for 37 years from 41 BC to 4 BC. According to the Gospels of Matthew and Luke, Jesus was born during his reign (Matthew 2:1; Luke 1:5). According to the Gospel of Matthew, Herod ordered the young children in Bethlehem to be slaughtered when he found out about the birth of Jesus (Matthew 2:16). Josephus summarizes his reign in Antiquities 17.8.1:
When he had done these things, he died, the fifth day after he had caused Antipater to be slain; having reigned, since he had procured Antigonus to be slain, thirty-four years; but since he had been declared king by the Romans, thirty-seven. A man he was of great barbarity towards all men equally, and a slave to his passion; but above the consideration of what was right; yet was he favored by fortune as much as any man ever was, for from a private man he became a king; and though he were encompassed with ten thousand dangers, he got clear of them all, and continued his life till a very old age. But then, as to the affairs of his family and children, in which indeed, according to his own opinion, he was also very fortunate, because he was able to conquer his enemies, yet, in my opinion, he was herein very unfortunate.
Tacitus’ mentions Herod in one section of his work:
The Histories 5.9:
The royal power, which had been bestowed by Antony on Herod, was augmented by the victorious Augustus. On Herod’s death, one Simon, without waiting for the approbation of the Emperor, usurped the title of king. He was punished by Quintilius Varus then governor of Syria, and the nation, with its liberties curtailed, was divided into three provinces under the sons of Herod.
Herod the Great willed his kingdom to three of his sons, Herod Archelaus, [Herod] Philip, and Herod Antipas as Josephus relates (Antiquities 17.8.1:):
And now Herod altered his testament upon the alteration of his mind; for he appointed Antipas, to whom he had before left the kingdom, to be tetrarch of Galilee and Perea, and granted the kingdom to Archclaus. He also gave Gaulonitis, and Trachonitis, and Paneas to Philip, who was his son, but own brother to Archclaus by the name of a tetrarchy; and bequeathed Jarnnia, and Ashdod, and Phasaelis to Salome his sister, with five hundred thousand [drachmae] of silver that was coined.
Herod Archelaus is only mentioned once in the New Testament in Matthew 2:22 where he is identified as the ruler of Judæa:
But when he [Joseph] heard that Archelaus was reigning over Judea instead of his father Herod, he was afraid to go there. And being warned by God in a dream, he turned aside into the region of Galilee.
According to Josephus, Joseph was right to fear Archelaus because soon after the death of Herod Archelaus had 3,000 people killed (Antiquities 17.9.3). Josephus also says the Archelaus was the ruler of Judea (Antiquities 17.11.4)
[Herod] Philip is mentioned once or four times in the Gospels (Luke 3:1 and possibly Matthew 14:3; Mark 6:17; and Luke 3:19). The issue about who is being referred to in the latter three references surrounds who “Philip” is. If it is Philip the Tetrarch (the Philip that Tacitus refers to) then either Mark and Matthew are incorrect in claiming that Herodias was formerly married to him or Josephus is incorrect in claiming that Herodias was formerly married to Herod II, the son of Herod the Great. Another option is that Herod II was really called “Herod Philip.” And that Josephus is correct in calling him “Herod” and the Gospel writers are correct in calling him “Philip.” Herod the Great’s family tree is very confusing, with people being called the same names numerous times, so it seems plausible that any of the above possibilities could be correct.
Herod Antipas is mentioned dozens of times in the Gospels. It was he who beheaded John the Baptist for criticizing his marriage with Herodias (Matthew 14; Mark 6; Luke 9), and according to Luke mocked Jesus before sending him back to Pontius Pilate (Luke 23). He is also mentioned once in Acts 4:27.
These three sons are mentioned by Tacitus, but not by name, in the previous quote:
The Histories 5.9
He was punished by Quintilius Varus then governor of Syria, and the nation, with its liberties curtailed, was divided into three provinces under the sons of Herod.