The Babylonian Exile began in 597, when the Babylonians conquered the Davidic southern kingdom of Judah, deporting the king, the royal family, the nobles, the warriors and the artisans. The conquest was completed in 586 B.C. with the destruction of Jerusalem, including the Temple. Most of the remaining Jews were deported at that time, except for some of the poorest who stayed on to till the land (2 Kgs. 25:12).
The Babylonian Exile is particularly significant in Jewish history because the Jews could not perform their prime religious service: offering sacrifices to God in the Temple in Jerusalem.
King Cyrus of Persia liberated the Jewish people from Babylon in 538 B.C., permitting them to return to Jerusalem to rebuild the Temple (Ezra 1:1-4). Cyrus is mentioned in Isaiah 44:28 and 45:1ff. Because he liberated the Jews, he is referred to as God’s anointed (Is. 45:1).
The rebuilt Temple was dedicated in 516 B.C., and so the prophesied 70-year exile that Jeremiah prophesied (Jer. 25:11; 29:10) can be understood as the period when there was no Temple worship (586 B.C. to 516 B.C.)