I remember reading that most of the vast atrocities brought before the war crimes tribunal happened after the NATO bombings, which only increased the violence. (edit: found the article: http://www.chomsky.info/articles/200005--.html)
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Kosovo has been a problem for Serbia/Yugoslavia for almost a century. It's not something that popped out of thin air during the 90s. But communist government had different approach and tried to appease Albanians who lived in Kosovo. Things changed with Milosevic (he came to power in 1987), that is when mass killings started. I'm fairly sure more people has been killed before NATO bombing. After NATO bombing Serbia lost most of the influence, Serbian minority fled the territory because "terrorists" or fighters were raiding their homes. Doubt that Serbian government could organize mass killings of Albanian civilians after NATO bombing, country was too weak, that is why Milosevic capitulated. Serbian people didn't know any of that in the beginning, because Milosevic was a tyrant and common people were busy with different matters (how to survive the war, inflation, sanctions, criminals...)
Whole thing started during Ottoman Empire, both Serbs and Albanians were part of Ottoman Empire for centuries and held some pretty important positions. As Ottomans weakened, they pushed out former non muslims away from positions of power. People who live in Kosovo and consider themselves Albanians are actually descendants of former Slavic converts to Islam. That's the true reason for strong hatred between them. True Albanians could never hate Serbs (and vice versa) like converts did. There is a saying but dunno how to properly translate it. It goes something like this: A convert is worse than a Turk. And it's very true, because those who did the worst crimes in many wars during past centuries were always some kind of converts.
And as time passed, Kosovo Albanians grew in numbers (thanks to their religion and huge losses Serbia had during both World Wars) and they became majority. Serbs who lived in Kosovo didn't care much about it, mostly used it for their own gain. Now everyone in Serbia is crying how "Kosovo is heart of Serbia" but truth is they didn't give actual fuck what will happen to Kosovo, they just exploited it.
Fun fact that many people don't know is that both Croatians and Serbs in the beginning were Slavs who lived on borders and were mainly soldiers, whose role was to protect "Slavic Empire in the making" from outsiders. That is why they fought so many wars in history, which is unusual for such smallish countries.