I've tried to work out the relationships between the different kings of the 6th to 4th Centuries. Here's my effort (thanks to the highly reliable information source of wikipedia).
The main reason is (going by the post two below) trying to understand what's happening in Daniel. The kings he mentions are Nebuchadnezzar, Belshazzar his son, Darius the Mede son of Xerxes (Ahasuerus), and Cyrus the Persian (in that order).
To explain the diagram as it relates to Daniel, Nebuchadnezzar is the king who was at the head of the Babylonian Empire as the Assyrians were finally finished off. Three kings later, Nabonidus usurps the throne, and while hanging out in some desert oasis, gets his son Belshazzar to look after Babylon while he's gone. Calling Belshazzar Nebuchadnezzar's son is then a literary device, to make us compare father with son, to see if he would learn from his father's mistakes and humble himself before the one true God (he doesn't).
The gap into which the Danielic Darius should slot into is the one between Nabonidus/Belshazzar and Cyrus. The fact that there is no gap, that the Medes never ruled Babylon (although Cyrus was half-Median), and that the Dariuses we know of came much later means this is a literary riddle, rather than an historical one. That is, why 1) invent a kingdom and a king, and 2) why give him the name Darius and the father Xerxes (Ahasuerus)? I'll proffer my suggestions below:
1. According to commentators, a four kingdom model was quite the thing back in the day. Being in the time of the kingdoms of Alexanders successors (the Diadochi), yet using stories from the Babylonian era, leaves only three kingdoms - Babylon, Persia, Greece. Media was a kingdom north and east of Babylon, and were pretty big, so from a literary perspective, Media seems a pretty good idea.
2. Darius is a pretty well known name, there being three kings with that name, and the names Xerxes and Artaxerxes (i.e. Xerxes with an 'Arta' tacked on) similarly so. So it's a pretty common name, but there has to be more. Well, Darius III, as you can see from the diagram, is an epoch finishing guy. He was the last of the line, and after him a new mob took over. Less importantly, his familial connection with the dynasty is a bit tricky/murky. Therefore, being relatively unattached, yet still important, his name would seem to be the most appropriate for a literary second kingdom.
Let me know what you think.
If I'm in a particularly masochistic mood I'll have a crack at the successors, that is, the Seleucids and the Ptolemies, to complete the table all the way to the 'abomination of desolation', that is, the misdeeds of Antiochus IV Epiphanes in the 2nd Century.