Judea was the name give to the land of the former Kingdom of Judah by the Greeks and the Romans, and is the term used in the New Testament. Judah was conquered by Babylonia in 586 BC, (2 Kings 25; 2 Chronicles 26; Jeremiah 52; Lamentations; Daniel 1) and the books of Ezekiel, as well as the first half of the book of Daniel, were set during the Babylonian Exile. Babylon was in turn conqured by Persia under Cyrus the Great in 539 BC (as prophecied by Isaiah 44:28-45:25). The books of Ezra, Nehemiah, Esther, Daniel, Malachi, Haggai, and Zechariah all lived under Persian rule.
The term "Judea" came into use in the time of Alexander the Great, who conquered Persia in 323 BC. Alexander's empire was divided between his generals following his death in 323 BC. Judea was then ruled in sucession by the Ptolmic (Egyptian) and Seleucid (Syrian) empires before becoming an independent Kingdom under the Maccabees, who ruled from 165 BC to 63 BC.
In 63 BC, Pompey the Great conqured Judea, which became a client kingdom of the Roman Empire. From 6 AD to 135, Judea was under direct Roman rule. Judea became part of Iudaea Province along with Samaria and Idumea (known in ancient times as Edom).
Following Bar Kokhba's revolt in 135, the Roman Emperor Hadrian expelled most Jews from Judea, and began using the name "Palaestina" (part of the province of Syria Palaestina) to describe all the land of Israel.
The legacy of Hadrian's action continues today in the disputes between Palestinians and Israelis. The Nation of Israel uses the term "Judea and Samaria" to refer to the land claimed by the Palestinian Authority, which most of the world refers to as the West Bank.