Kosovo (capital city: Pristina) was formerly a part of Serbia. Although considered by Serbs to be the cradle of their civilisation (seemingly because in some mediaeval battle there the Serbs were stuffed out of it by the Turks) the area is predominantly inhabited by ethnic Albanians. In the Yugoslav period, the area became an autonomous region within Serbia, but it was never raised to the status of a full constituent republic.
Kosovo's history and the rise and fall of Slobodan Milosevic are closely intertwined. Milosevic shot to prominence by embracing Serbian nationalism and the cause of the Serbian minority in Kosovo. On achieving power in Serbia, he succeeded in closing down the region's autonomous government, shutting the ethnic Albanians out of public life. In the early 1990s, though, armed Kosovar rebels struck against Serbian rule, and Milosevic's attempt to crush them triggered the NATO bombing campaign that effectively forced a Serbian withdrawal from the region, fatally undermining Milosevic's credibility.
Kosovo thereafter assumed a somewhat anomalous status. The international community basically ran Kosovo as protectorate while preserving the fiction that it was still part of Serbia. Eventually, though, Kosovo was allowed to declare independence in 2008. There was much grumpiness about this in Serbia (and among ethnic Serbs in Kosovo), but the Serbs were unable to prevent this development. Because of the general distaste in international law and politics for secessionist regimes, Kosovar independence was justified on the convoluted grounds that Milosevic's 1994 crackdown constituted an effective Serbian repudiation of sovereignty over the province.
Now, one might wonder why I am bothering to list Kosovo as a phantom country. It does, after all, have a lot of international recognition, including by three permanent members of the UN Security Council. Kosovo's status nevertheless remains somewhat anomalous, for a number of reasons. Firstly, its state apparatus is still a bit ramshackle, and the country remains dependent on civil and security support from the international community. One could argue, therefore, that despite the relatively wide recognition afforded to it, Kosovo's independence is actually notional, with the region remaining a protectorate. Another problem is that although Kosovo has received plenty of recognition, many other countries actively reject it as an independent state. The Serbian state continues to maintain that it has jurisdiction over Kosovo. Although the Serbs do not really count for much, they are pals with the Russians, whose Security Council veto stands in the way of Kosovar membership of the United Nations. Spain, meanwhile, bedevilled by its own would-be secessionists, has also declined to recognise Kosovo, and may well block any move towards Kosovar membership of the EU. Kosovo is therefore likely to remain outside the world of key international organisations for some time.
Kosovo also has internal problems. The Serbian minority are not that taken with separation from the rest of Serbia. Serbs in the border areas adjacent to Serbia-proper have effectively seceded from Kosovo, rejecting Pristina's authority in favour of Belgrade. Relations between Serbs and Albanians in the rest of the country remain tense, partly triggered by memories of intercommunal violence during the Milosevic years.
It is hard to know what the future holds for Kosovo. One possibility is that some kind of comprehensive Balkan settlement will see Pristina and Belgrade make friends as they jointly move to EU candidacy and Kosovo becomes fully accepted into the family of nations. For this to happen, though, it will be necessary for Kosovo to build an effective administration and to achieve some kind of rapprochement with its internal Serbian minority. It would not surprise me if the areas abutting Serbia succeed in seceding from Kosovo, or are at least allowed to permanently remain under Serbian administration even if showing up on maps as part of Kosovo.
An aside – there is apparently very little likelihood of Kosovo ever becoming part of Albania. Although Kosovo has a large majority of ethnic Albanians, ethnic Albanians do not seem to have the kind of pan-nationalist sentiment seen in some members of other ethnicities. There seems little or no interest in forming a Greater Albanian state out of Albania, Kosovo, and the bits of surrounding countries that have large Albanian populations.
Another aside – I think that ethnic Albanian Kosovars refer to their country as Kosova, but I am opting for the generally accepted international version of the country's name.