The deportations of the Hebrews to Babylon affected many thousands of lives, including well-known Bible characters such as Daniel, Ezekiel and Esther. Yet these deportations hinged almost entirely upon the actions and attitudes of three men Jehoiakim, Jehoiachin and Nebuchadnezzar.
Jehoiakim was the second son of Josiah king of Judah, his mother was Zebudah, the daughter of Pedaiah of Rumah.. He was born around 635BC under the name of Eliakim (Resurrection of God). Although we are told little of his early life we do know that when his father died it was his younger brother Shallum that was the peoples choice for king. He came to the throne in his 25th year (610BC) after Shallum, who was sympathetic towards the Babylonians, had been deposed by Pharaoh-Necho. As part of this manoeuvre Pharaoh changed Eliakim's name to Jehoiakim (avenging, establishing or resurrection of the Lord) and established that Judah should pay tribute to Egypt. Jehoiakim raised this tribute by laying a tax burden upon the people.
In the third year of Jehoiakim's reign Nebuchadnezzar invaded and carried him away although he was later re-instated as a vassal king of Babylon.
History shows that Jehoiakim's ultimate downfall came because he chose to rebel against Babylon. It had seemed like a smart move, Nebuchadnezzar had suffered at the hands of Pharaoh-Neco and had returned home to Babylon, Jehoiakim seized the chance to throw off the Babylonian yoke and avoid paying the tribute. Indeed as events proved, the Babylonians were distracted, and rather than sending a main force straight away Nebuchadnezzar was forced to work through Chaldees, Syrians, Moabites and the Ammonites. Whilst this group didn't actually manage to take Judah during Jehoiakim's life they were able to devastate it.
The Bible doesn't actually tell us the final fate of Jehoiakim but some of the prophecies of Jeremiah (22:18-19, 36:30) are suggestive. Jehoiakim was to be unlamented, cast beyond the gates, left day and night, dragged and given the burial of an ass. One could imagine a siege in process, the attackers promise the besieged some reward if they depose their king, and he is taken, killed and thrown over the walls. The body is then almost ceremonially mistreated.
Of course, whilst we can view Jehoiakim in the light of history, to find out what really happened we have to view history in the light of God. As always this is most illuminating. 2 Ki 24:3 shows that whilst Nebuchadnezzar must have thought he was acting on his own initiative it was actually God moving, against the kings of Israel.
Regrettably Jehoiakim is proof that a Godly father does not necessarily result in a Godly son. The Bible woefully summarizes the situation with he did that which is evil in the sight of the Lord (2 Ki 23:37). Jeremiah gives some more detail in chapter 22; there he suggests that Jehoiakim lived in luxury but that he obtained his riches by unfairly treating the poor. Jeremiah also shows the root of Jehoiakim's problem; it wasn't that he didn't know the ways of God it is that he didn't want to. That is the only real explanation of Jeremiah 36 where Jehoiakim burnt the words that God had sent to him. This is even more amazing when you think this is only a year or two after his capture and re-instatement by Nebuchadnezzar!
Jehoiachin (otherwise known as Coniah and Jeconiah) was the son of Jehoiakim and Nehushta, the daughter of Elnathan of Jerusalem. He reigned after the death of his father for a period of three months. It is possible that he was co-regent with his father for a decade before that, this would explain the discrepancy between 2 Ch 36:9 and 2 Ki 24:8 where he is cited as being 8 & 18 respectively when he began to reign.
He again did evil in the sight of the Lord and was forced to surrender to the Babylonians. This he did and spent the rest of his life in exile in Babylon. The first 37 he spent in imprisonment before being liberated by Evil-merodach who gave Jehoiachin eating privileges at his table.
Jehoiachin was the last direct heir of the Jewish crown and Jeremiah predicted that he would have no seed upon the throne. In one sense this happened, in another God showed his sovereignty. Jehoiachin means 'appointed of God'; he wasn't just the last in a long line of seeming mistakes. He was God's chosen vessel, even if he didn't obey God! Thus, lo and behold, in Matthew 1:11 Jehoiachin appears again in the ancestry of the Lord himself. 
The final player in the drama of deportation was Nebuchadnezzar. Nebuchadnezzar came to the Babylonian throne in 604BC upon the death of his father Nabopolassar. He was an able military commander having already won a decisive victory over Pharaoh in Carchemish  Like his father he was an empire builder, and was willing to leave kingdoms with a degree of sovereignty provided they would become a subservient part of his kingdom. His name means, 'Nebo protect the crown', although he self-styled himself as "Nebo's favourite". His reign finally ended in its 43rd year, his 84th year of age.
There is much that history says about the strategic importance of Babylon during Nebuchadnezzar's reign and Nebuchadnezzar has the distinction of being the most powerful gentile king that ever lived -- at least from a biblical perspective. Yet when looked at from heaven's viewpoint he was really just a pawn, or more accurately a servant!
The God of Heaven had a chosen people; he had chosen a line of kings to rule those people. From a human perspective Jehoiakim had made a strategic political move and got unlucky in facing the most successful king of the era. From a human perspective Jehoiachin was unlucky enough to get thrown into an impossible situation and did pretty well to get out alive. From a biblical perspective they both made the same mistake, they forgot God, or rather they chose to ignore him.
There is little we can learn from these examples of direct practical benefit, we are not kings and are unlikely to have to withstand, or provoke a siege. Indirectly the lesson is simple: ignore God, ignore his warnings and eventually something will come against you far bigger than anything you can handle. It may look like bad luck, it isn't.