Even after years of researching Luxembourg’s history, I still can’t tell you which countries controlled Luxembourg when. And that’s hugely important, as the controlling countries have Luxembourg’s records for the period.
However, the German Genealogical Society offers a page that can help. Their Luxembourg profile holds a short history of the country, online resources (beware – the list is outdated), and books referencing the country’s history. While only the history is still accurate, it’s definitely worth a look if you’re just beginning Luxembourg research.