As we know, King David wanted to build a Temple which would house the Ark of the Covenant and be the place of prayer and worship for the Jews. After he captured Jerusalem, he moved the Ark there. As the site for the Temple he chose Mount Moriah, where Abraham had built an altar to sacrifice his son Isaac. When God, through the prophet Nathan, told David that, because he had spilled so much blood, he was not to build the Temple, this task was left to his son Solomon.
Solomon had the Temple built over a period of years and it was completed in 957 BC. The building itself was not large, but it had an extensive courtyard. It faced eastward and had three rooms of equal width: a porch or vestibule, the Holy Place for religious services, and the Holy of Holies, where the Ark was kept. The Holy of Holies was considered the dwelling place of the Divine Presence, and only the High Priest could enter it, once a year, on the Day of Atonement, Yom Kippur.
Early in the sixth century BC, King Nebuchadnezzar II of Babylon went with his troops to Jerusalem, laying siege to the city and entering it. He removed the treasures from the Temple, including the Ark of the Covenant, and took many of the Jews into captivity. In 586 BC he destroyed the Temple completely. In 538 BC, Cyrus II of Persia conquered Babylon and issued an order allowing the exiled Jews to return to Jerusalem and to rebuild the Temple. The work was completed in 515 BC. This second Temple was a modest version of the first one, surrounded by two courtyards with chambers, gates and a public square.
Another important moment in the history of the Temple came in the third and second centuries BC during the Persian and Hellenistic domination of Israel. In 169 BC the Seleucid ruler Antiochus IV Epiphanes plundered the Temple, and in 167 he desecrated it by having sacrifices to Zeus offered there. This final act touched off the Hasmonean revolt by the Maccabees. In 164 BC, Judas Maccabeus cleansed and rededicated the Temple, an event now celebrated annually in the festival of Hanukkah.
In the first century BC the Romans occupied Palestine, and in 63 BC Pompey entered the Holy of Holies, thereby desecrating it, but he left the Temple intact. Nine years later, in 54 BC, Crassus looted the Temple treasury.
As you mentioned in your question, King Herod the Great (37-4 BC) had an important role to play as regards the Temple, renovating and enlarging it. Construction began in 20 BC and lasted for 46 years. The area of the Temple Mount was doubled and surrounded by a retaining wall with gates. The Temple itself was raised, enlarged, and faced with white stone. The new Temple square served as a gathering place, and its porticoes sheltered merchants and money changers. A stone fence and a rampart surrounded the consecrated area, which was forbidden to Gentiles.
The Temple had three principal parts: the Court of Women, the Court of Priests with its altar of sacrifice, and the Holy of Holies, separated off by a great curtain. It was in this Temple that Jesus and the apostles often went to pray and to preach the Gospel. Surrounding the Temple proper was the Court of the Gentiles.
A final moment in this history came in the year 70 AD, when the Roman General Titus destroyed the Temple completely. It was never rebuilt. All that remained of the Temple Mount was a portion of the Western Wall, now called the Wailing Wall, a focus of Jewish prayer to this day.