As far as I know, they have a unique language in comparison to their neighbors. Were they a tribe that moved into the region during the migration period, are they the descendents of the Epirots or Illyrians, or do they have another origin?
The theory that Albanians were related to the Illyrians was proposed for the first time by the Swedish historian Johann Erich Thunmann in 1774. The scholars who advocate an Illyrian origin are numerous. There are two variants of the theory: one is that the Albanians are the descendants of indigenous Illyrian tribes dwelling in what is now Albania. The other is that the Albanians are the descendants of Illyrian tribes located north of the Jireček Line and probably north or northeast of Albania
The only thing that is scientific proved based on various genetic studies that have been done on the European population, some of them including current Albanian population, Albanian-speaking populations outside Albania, and the Balkan region as a whole is that the two haplogroups most strongly associated with Albanian people (E-V13 and J2b) are often considered to have arrived in Europe from the Near East with the Neolithic revolution or late Mesolithic, early in the Holocene epoch (11,700 calendar years BP). From here in the Balkans, it is thought, they spread to the rest of Europe. More recently, Lacan et al. (2011) announced that a 7000 year old skeleton in a Neolithic context in a Spanish funeral cave, was an E-V13 man. (The other specimens tested from the same site were in haplogroup G2a, which has been found in Neolithic contexts throughout Europe.) Using 7 STR markers, this specimen was identified as being similar to modern individuals tested in Albania, Bosnia, Greece, Corsica, and Provence.