Alright, so first off: what was the Kalmar Union? The Kalmar Union was a union between Denmark, Sweden and Norway. Queen Margrete, mother of the deceased chosen king Oluf of Denmark and Norway, was chosen by Swedish noblemen in 1389 to be the ruler of Sweden as well and thus replace the German Albrekt of Mecklenburgh, who was very disliked. This union wasn't made fully 'official' until a meeting in Kalmar in 1397, during which her adoptive son Erik of Pomerania was crowned as king.
This meeting is disputed, not whether it happened or not, but about what was actually decided. There are two documents from this meeting. The first one states the Erik has been made king of all three countries, the document is written on pergament and properly sealed. The other one is the one called the "union letter", which is only preserved in an incomplete letter with a sigil, written on simple paper. In this one it says that a full union was created in which mutual kings would be chosen in the future, but also that each country would keep it's own laws. Both a Swedish and a Danish historian has concluded that the union letter was more or less a compromise made by the country councils, but that it's the coronationletter that's the real one, approved by queen Margrete.
Erik of Pomerania co-ruled with queen Margrete from 1397 to 1412 when Margrete died. During that time nothing particular happened, standard politics you might say. However, when Margrete died, Erik was left as sovereign ruler of Denmark, Sweden and Norway. The politics had increasing costs and the common people were the ones who had to pay the price. The situation was a problem for the trade and especially then for the Hanseatic [league] cities Lübeck and Hamburg. When Erik then in 1420 financed the war-politics by raising the toll for passage through Øresund/The Sound it lead to war with the Hanseatic league. That war in turn lead to more taxes, which of course spread discontent through the union.
The Engelbrekt rebellion in Sweden in 1434 is generally seen as the beginning of the end for the union. Together with the council and commoners, the mountain men accused king Erik of a list of things, among which was excessive violence from his bailiffs. The peasants blamed the bailiffs for the taxes, the church was worried about the kings power in electing new bishops and when the leader of the rebellion, Engelbrekt, was dead, the council took control over the rule of Sweden. Inofficially the Kalmar union then ended in 1434. Erik wasn't dethroned in Denmark until 1439 and Norway in 1440. There was an attempt to reform the union with the coronation of Christoffer of Bayern who had ties with the royal houses of all three countries, but he died suddenly in 1448.
At his death, Denmark chose a Christian of Oldenburg (Christian I) as king while Sweden chose the nobleman Karl Knutsson Bonde (bonde=peasant, but it was a family name). Karl Knutsson Bonde was king of Sweden three times during his life and generally he can be associated with a rather turbulent kingship period in Sweden, during which a myriad of kings sat on the Swedish throne, including Christian I. Technically, the Kalmar union was still in effect during the years when Christian I was on the Swedish throne (he was king of Denmark and Norway until 1481 when he was succeeded by his son, Hans).
Christian I was defeated in the battle of Brunkebergstorg in 1471 and replaced as the ruler of Sweden by Sten Sture the Elder (though, not king). The Kalmar union was once again technically reunited in 1497 when king Hans got access to the Swedish throne. He was only union king for four years though, because after a rebellion in 1501, he was dethroned.
The definitive end of the Kalmar union came in 1523 (or 1537) depending on how you count. The union did not end when Hans was dethroned after the rebellion and when his son Christian II succeeded him in 1513 he made attempts to retake the Swedish throne. In 1518 he failed an attempt to conquer Stockholm. Negotiations were started but never came to a result so Christian II sailed back to Denmark with a hostage - of which Gustav Eriksson Vasa was part. The Swedish noblemen had been a thorne in the side ever since the days of Erik of Pomerania and in 1520, Christian II tired of their inability to unite. On November 4, 1520 Christian II was crowned king of Sweden and on that same day, in one of the most famous events in Swedish history, he decapitated every single member of the Swedish nobility present in Stockholm.
However, as we have seen, a son of one of the Swedish noblemen, Gustav Eriksson Vasa, was held hostage in Denmark at the time and thus not present in the bloodbath. As you might imagine, Christian II wasn't much liked in Sweden, but he was also very disliked in Denmark and in 1523 there was a rebellion so Christian had to flee to the Netherlands. In Sweden, Gustav Eriksson Vasa was crowned king in the same year.
The story does not end here though. When Frederik I (who became Danish king after the rebellion in 1523) died, there was no accepted succeeder. The result was a war between the rightful heir to the throne, Frederik I's son Christian III, and count Christoffer of Oldenburg from Lübeck. Gustav Vasa supported Christian III and together they concluded a peace after a seabattle won in 1535. The official end of the Kalmar union came in 1537. In 1537 Norway was proclaimed to be a part of Denmark and no longer a separate kingdom, but the Danish kings kept treating Norway as such. Sweden had been a separate kingdom since 1523.
Also in 1537, the church lost its power in Sweden when a centrally controlled church was formed under the ruling king. Bishop were no longer appointed by an arch bishop but by the king. Or simplified, Sweden switched from Catolicism to Protestantism. The same switch came in Denmark in 1536, in Norway in 1537 and on Iceland in 1550. Small fact: During the same time period as the problems with king Erik happened, similar problems with bailiffs existed in France and England, which is were the legend of Robin Hood started. Erik of Pomerania's queen, Filippa, was the daughter of king Henry IV of England during the Hundred Year's war; she's one of the most powerful women in Swedish history, but very unknown.
Sources:
Gustafsson, H. (2007), Nordens Historia: En Europeisk Region Under 2000 År, pp. 74-90.
Lindkvist, T. & Sjöberg, M. (2010), Det Svenska Samhället 800-1720: Klerkernas och adelns tid, pp. 174-201.