Several successors to Nebuchadnezzar are not mentioned in Scripture, not even the last king of Babylon, Nabonidus (556-539).  However, his son Belshazzar (553-539), who was co-regent, is famous for hosting the dinner during which mysterious writing appeared on the wall.  Daniel interpreted this writing as the judgment of God (Dan 5:24-28).  Belshazzar was killed when Babylon fell to Cyrus, king of the Medo-Persian empire (Dan 5:30-31).  For many years, historians questioned the existence of Belshazzar, but his name was found on the Nabonidus Cylinder (see artivle in Wikipedia).  Daniel outlived all these kings.

        

Cyrus ruled over Persia from 559 to 530, over Babylon from 538-530.  The first year of his reign over Babylon, he issued his famous decree authorizing the Jews in exile anywhere throughout his kingdom to return to Jerusalem and rebuild the Temple (Ezra 1:1-4, Ezra 6:3-5).

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         "It might seem surprising that so great a conqueror as Cyrus should so interest himself in the affairs of people as politically unimportant as the Jews.  But we know that his decree was only an illustration of his surprisingly moderate general policy, a policy followed by most of his successors.  Cyrus was one of the truly enlightened rulers of ancient times.  Instead of crushing national sentiment by brutality and deportation as the Assyrians had, it was his aim to allow subject peoples as far as possible to enjoy cultural autonomy within the framework of the empire"  (Bright, John. A History of Israel, 2nd ed. Philadelphia: Westminster, 1972, p. 362).