I'm sure someone far more knowledgeable than I will jump in, but the history of the former Yugoslavia has a bit of an academic obsession for me. It was watching events unfold on the TV that made me want to be a journalist. My dad was in the army and I believed everything he said about the world, I remember sitting on the carpet watching AKs rattle in news footage. I turned to him and said "Dad, who are the good guys?" He looked away and then replied, "I'm not sure."
Even throughout the Tito period, the various cultural and economic issues in each constituent republic had been pulling them in different directions. Tito's strategy of carefully balancing national aspirations and influence staved off collapse (along with Western cash for turning its back on the Soviet Bloc) but turned the whole edifice into a teetering tower that threatened to topple as each piece was removed from the base.
Milosevic's rise mirrors Putin's in some ways, and the situation in Crimea, Georgia, Eastern Ukraine etc hold up a few similarities. Milosevic was a fairly unremarkable part functionary who seized upon Serbian nationalism as a way to rocket up the polls to leadership of Serbia (and the Serbian voting bloc in Yugoslavia's precarious sorta-federal system, so Slovenia, Bosnia, Croatia and Macedonia could be easily countered by Serbia, Montenegro and the autonomous provinces of Serb-dominated - politically at least- Vojvodina and Kosovo).
Slovenia voted for independence and after a fairly lukewarm tussle was able to cede from Yugoslavia without significant bloodshed. Slovenia didn't have a meaningful Serb minority and culturally/linguistically was much closer to Central Europe anyway. Croatia was next up, but the political situation was much closer to the boil with a fiercely nationalist Croatian president (arguably every bit as cynical as Milosevic) and a entrenched Serbian minority who threw up roadblocks and declared their own breakaway provinces, which were shored up by weapons from the demobilised Yugoslav army and Serbian volunteers from other provinces, many of them career criminals. Serbian nationalists saw their countrymen under threat, and propaganda played up Croatia's fascist credentials in World War II.
As the conflict in Croatia began to wind down, Bosnia and Herzegovina went down the same basic path, but with a population much more neatly divided between Serbs, Croats and Bosniaks (Bosnian Muslims), it eventually erupted into a bloody three-way civil war, especially in the later phase when Croats and Bosniaks began to fight in Herzegovina. The end game for the Bosnian Serbs, was to carve off a chunk of Bosnia and attach it to Serbia proper (and to that end 'cleanse' their territories of any ethnicity that would make this problematic), Serbia's end-game was not to preserve Yugoslavia as it was imagined decades earlier, but to preserve a rump Yugoslavia dominated by Serbia - which to the nationalists seemed like a fair trade off. Less overall territory, but greater total control.
Croatia - like Slovenia a wealthier more European-looking province - wanted all the things Europe had, but unlike Slovenia, while the nationalists wanted to scoop up all the regions dominated by Croats - such as Herzegovina.
Traditionally Serbs dominated the army and as the Yugoslav National Army (JNA) answered to Milosevic, forces 'officially' withdrew from Bosnia and Croatia but often left their artillery and weapons in Serb enclaves, or allowed Serbs to desert and take up the fight. This created a cruel imbalance where relatively small separatist forces had access to better weapons and training than the new government forces who were generally just police, volunteer militia or glorified crime gangs given status as 'special police' units. What's more, the international arms embargo meant no new hardware was entering the former Yugoslavia (which, btw, counted arms as one of its major exports) - maintaining murderous status quo and forcing the Croatian and Bosnian governments to smuggle in weaponry illegally.
The religious element made things fiercer still, inviting historical comparisons and twisting public opinion in the eye of the beholder. European volunteers - including Brits- fought for the Croatian cause to defend Catholicism, while Greeks and Romanian volunteers crossed the border to fight for the Orthodox cause ("Serbia only has two friends," the maxim goes, "God and the Greeks."), while the plight of the Bosnian Muslims - though largely secular, this is Islam as a cultural rather than religious identity - attracted the attention of foreign Jihadis.
Kosovo and Macedonia (FYROM, if any Greeks are reading this!) are much simpler to explain. Kosovo is the historical 'heart' of Medieval Serbia and key to its national myth, but population shifts under the Ottoman Empire had left it dominated by Kosovar Albanians. A Serbian minority controlled the government and police and fiercely resisted any sniff of Kosovar nationalism. The Kosovar Liberation Army - partly out of cynicism after seeing the way the international community had turned on Serbia during the Bosnian War and partly out of realism after seeing the atrocities committed against their neighbouring Muslims - kicked off an insurgency partly designed to provoke a Serbian overreaction, which it did.
FYROM, the last to opt out of Yugoslavia, didn't have a significant Serb population, but had a Kosovar dominated fringe (swelled by refugees from Kosovo) and at after a brief, cack-handed counter-insurgency by Macedonian police against the Albanian National Liberation Army (NLA) invited the international community in to resolve it.
That is a potted version of what everyone wanted and why they went at each other so horrendously. I've glossed over a great deal, and I apologise for any omissions or fudging of details. I'm sure one of the duly appointed grown ups will be along to put me right! :)
A good place to start is the BBC documentary The Death of Yugoslavia, which is old but still very good and filled with revealing interviews from literally everyone.