The Oxford Bible Commentary points out that the move from Zerubbabel to Ezra is a move from discussion of the physical restoration to the spiritual. Further, as in the books of Ezra and Nehemiah, the gap in the time periods of something like 70 to 120 years is not made explicit. (p 203ff).
Esdras (from now on, I think I'll go ahead and call him Ezra), a scribe, was sent by the king along with other Israelites, priests, holy singers, porters, and ministers to live in Judea and Jerusalem and there to abide in the law of the Lord. He directed the treasurers of Syria and Phenice to give them whatever resources the needed and that no taxes be levied on the temple professionals.
One matter that arose--Some of their sons had married Gentile women. Ezra reacted strongly, went into mourning. He tore his clothes, pulled out his hair from his head and beard, fasted, and sat in mourning all day. Then, he rose and prayed, "O Lord, we are sinners, but you have shown us mercy. We now have been allowed to return home and to rebuild your temple. Yet, we have disobeyed your commandments.
As he lay flat on the ground weeping, a large number of men, women, and children gathered around him, and they were weeping too. One of them called out, O Ezra, we have sinned against the Lord God, we have married foreign women. Let us now make an oath that we will put away all our heathen wives and their children.
Ezra agree that they should do this.
Today also we are confronted with religious leaders preaching against some marriages.