Until 03 October 2015 Luxembourg was subdivided into three districts, as they were: Diekirch, Grevenmacher and Luxembourg. Those districts never represented what in Belgium and the Netherlands for example are the so called provinces, or the Bundesländer in Germany and Austria.
Those three districts were abolished then, but the cantons still exist: Capellen, Clervaux, Diekirch, Echternach, Esch-sur-Alzette, Grevenmacher, Luxembourg, Mersch, Redange, Remich, Vianden and Wiltz.