Easton's 1897 Bible Dictionary:

Darius
   the holder or supporter, the name of several Persian kings. (1.)
   Darius the Mede (Dan. 11:1), "the son of Ahasuerus, of the seed
   of the Medes" (9:1). On the death of Belshazzar the Chaldean he
   "received the kingdom" of Babylon as viceroy from Cyrus. During
   his brief reign (B.C. 538-536) Daniel was promoted to the
   highest dignity (Dan. 6:1, 2); but on account of the malice of
   his enemies he was cast into the den of lions. After his
   miraculous escape, a decree was issued by Darius enjoining
   "reverence for the God of Daniel" (6:26). This king was probably
   the "Astyages" of the Greek historians. Nothing can, however, be
   with certainty affirmed regarding him. Some are of opinion that
   the name "Darius" is simply a name of office, equivalent to
   "governor," and that the "Gobryas" of the inscriptions was the
   person intended by the name.

     (2.) Darius, king of Persia, was the son of Hystaspes, of the
   royal family of the Achaemenidae. He did not immediately succeed
   Cyrus on the throne. There were two intermediate kings, viz.,
   Cambyses (the Ahasuerus of Ezra), the son of Cyrus, who reigned
   from B.C. 529-522, and was succeeded by a usurper named Smerdis,
   who occupied the throne only ten months, and was succeeded by
   this Darius (B.C. 521-486). Smerdis was a Margian, and therefore
   had no sympathy with Cyrus and Cambyses in the manner in which
   they had treated the Jews. He issued a decree prohibiting the
   restoration of the temple and of Jerusalem (Ezra 4:17-22). But
   soon after his death and the accession of Darius, the Jews
   resumed their work, thinking that the edict of Smerdis would be
   now null and void, as Darius was in known harmony with the
   religious policy of Cyrus. The enemies of the Jews lost no time
   in bringing the matter under the notice of Darius, who caused
   search to be made for the decree of Cyrus (q.v.). It was not
   found at Babylon, but at Achmetha (Ezra 6:2); and Darius
   forthwith issued a new decree, giving the Jews full liberty to
   prosecute their work, at the same time requiring the Syrian
   satrap and his subordinates to give them all needed help. It was
   with the army of this king that the Greeks fought the famous
   battle of Marathon (B.C. 490). During his reign the Jews enjoyed
   much peace and prosperity. He was succeeded by Ahasuerus, known
   to the Greeks as Xerxes, who reigned for twenty-one years.

     (3.) Darius the Persian (Neh. 12:22) was probably the Darius
   II. (Ochus or Nothus) of profane history, the son of Artaxerxes
   Longimanus, who was the son and successor of Ahasuerus (Xerxes).
   There are some, however, who think that the king here meant was
   Darius III. (Codomannus), the antagonist of Alexander the Great
   (B.C. 336-331).


Hitchcock's Bible Names Dictionary (late 1800's):

Darius, he that informs himself