Though it's controversial, most historians and linguists believe the Albanian people are the direct decendents of the Illyrian people. They live in the same area the Illyrians once lived, they speak an Indo-European language that could very easily be a descendant of the Illyrian's language (which was Indo-European) and their language contains many very old loanwords from Latin, which suggests a long period of cohabitation. Aside from that, the Albanian people and their government believe it quite strongly, which can be problematic as they use it to bolster their nationalism and irredentist claims.

Arguments against include the lack of linguistic evidence. There just aren't enough surviving Illyrian inscriptions. Nor Dacian or Thracian, either of which some linguists believe may be the origins of Albanian as well. There's also a historical tradition that regards the Albanians as recent migrants. This serves Slavic nationalist-irredentist arguments "they're invaders, we've been here longer!" Like the Albanian nationalist argument, it doesn't really prove anything either way, but it makes the debate more problematic.

There aren't actually any records of the Albanians before the 11th century, but they were already Christians by then, so make of that what you will. Most historians believe they're decendents of the Illyrians, Dacians, or Thracians. The debate revolves around which, but there just isn't enough evidence. Personally, I think the Illyrian argument makes the most sense.

For a source on the linguistic information, you can refer to Noel Malcolm's Short History of Kosovo: http://www.amazon.com/Kosovo-Short-History-Noel-Malcolm/dp/0060977752