After the collapse of the Socialist Federal Republic of Yugoslavia in 1991, four of its constituent republics broke away to form independent countries:

Incidentally, the SFRY constitution explicitly allowed the secession of its republics (albeit without specifying a means of doing so). This right was not extended to "nationalities" within a state, such as Kosovo and Vojvodina in Serbia, but I'm getting ahead of myself...

The name "Yugoslavia" ("South Slav Land") and thus the claim to the mantle of the SFRY -- including overseas monetary assets -- was retained by the rump state of Serbia and Montenegro, along with various claims of ownership over the other republics, leading to the Balkan War. In protest, for almost ten years nearly all nations refused to recognize this use of the name, referring to the nation simply as Serbia and Montenegro. Howeber, after the 2000 extradition of Slobodan Milosevic to the Hague to face a war crimes tribunal, the Federal Republic of Yugoslavia (under that name) was promptly admitted into the United Nations and the US (among others) established diplomatic relations.

But 'twas not be -- on March 14, 2002, the state known as the Federal Republic of Yugoslavia officially ceased to exist. Following the completion of arduous negotiations between Serbia and Montenegro, the two states are now known under the collective name Serbia and Montenegro (creative, yes?), maintaining a common foreign policy and seat in the UN General Assembly, but very little else. In 3 years time, Montenegro has the option of re-evaluating its situation and opting for full independence, and more likely than not the last of Tito's eternal ties of unity between Slav brethren will then be cut.