The state of Belgium has since 1968 had a perfectly straightforward, logically organised federal system of government.
As you will have surmised, Belgians come in a range of different versions, notably as regards language use (although the CIA factbook is misleading in that 11% of the population are not actually bilingual themselves - they just live in administratively bilingual areas). Unfortunately for the drawers of lines on maps, people do not choose where to live - or, indeed, who to live with - on exclusively linguistic grounds. In order to make provision for this, there are two parallel forms of authority below the Federal level.
Because lines have to be drawn on maps, and responsibilities taken for things that are located here rather than there, there are three Regions: Vlaanderen or Flanders (Dutch-speaking and mainly inhabited by the Flemish), Wallonie or Wallonia (Francophone and mainly inhabited by the Walloons, with a small German-speaking bit) and Brussels-Capital, an enclave within Flanders whose inhabitants are a cosmopolitan bunch with a French-speaking majority, but which is officially bilingual French-Dutch.
Because there are things which have to be dealt with on language lines, because language politics are rather touchy round here, there are also three Communities, the Flemish (Vlaamse Gemeenschap), the French (Communauté française) and the German-speakers (Deutschsprächige Gemeinschaft).
Beneath the regions there were eight and are now nine provinces (the province of Brabant, which straddled the border between Flanders and Wallonia, was split into Brabant Wallon and Vlaams Brabant in the late 1990s; the others are Antwerp, Hainault, Liege, Limburg, Luxembourg, Namur, East Flanders and West Flanders). A Belgian citizen thus lives in a province which is in a region and belongs to a community, which determines which elections he or she gets to vote in, etc. etc. The government of Brussels-Capital region also deals with things which fall within the responsibility of the provinces elsewhere.
So far so good. However, there are of course people who speak one language but live in a region that officially speaks something different. Municipalities where there are large populations (including, in some cases, an actual majority) of such misfits may be designated as "communes aux facilités" or "faciliteitensgemeenten" where it is permissible to conduct various bits of official business (and, believe me, there are plenty of them to conduct) in the "wrong" language, if you ask nicely first and are prepared to get in the slower moving queue. This is a perpetually contentious issue as the Flemish consider these facilities to be a transitional measure while incomers are adapting to the local way of life (and language), while the francophones treat it as a permanent provision.
To complicate matters slightly, the Flemish (who are more gung-ho about the whole affair) have decided to combine the Flanders Region and the Flemish Community into a single administrative entity, a move which was not wholly uncontroversial amongst the French-speakers of Brussels, not least because the joint Flemish Parliament actually sits in Brussels, while the two separate francophone community and Walloon regional assemblies are out in the sticks somewhere; this is exacerbated by the way that the outer suburbs of Brussels spill out into Flemish Brabant, where the locals are desperate to avoid being culturally overwhelmed by francophones and Eurocrats moving out of the city.
Simple enough, really.