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Northwestern Europe is a variously-defined northern area of Western Europe and a western area of Northern Europe.
Geographic definition 
Geographically, it is almost always used to include Great Britain, Ireland and the Benelux and Nordic countries (though possibly not Finland). It would normally exclude the Iberian peninsula, Italy, Switzerland, southern and eastern parts of France and Germany, and Austria. This usage is helpful when discussing issues of climate or biology.
Ethnographic definition 
Historically and linguistically, in "North-West Europe" the remaining major groupings are Celtic Europe, Germanic Europe, and the Finns. However there's no longer a sharp distinction as Germanic languages or Romance Languages have at least co-official status in all of the traditionally Celtic polities and the region has a history of Protestantism that differentiates it from its Mediterranean Latin or Eastern European Slavic neighbors. This leads to much the same definition as the geographical one above, but would tend to exclude France and southern Belgium including areas which retained Celtic elements into the Middle Ages. Measured by this attribute it would therefore be closer to the area shown on the map as Northern Europe plus the low countries and Northern Germany. The Nazis became champions of Northwestern European or Aryan supremacy.
World War II Theatre 
In British and Canadian military history, North-West Europe has been used to refer to the land campaigns in that approximate area during World War II. Two separate battle honours were awarded to regiments who took part in these campaigns "North-West Europe Campaign of 1940" and "North-West Europe Campaign of 1944-1945". The North-West Europe Campaign of 1940, during the Battle of France, was restricted to Belgium and the French Channel ports. The North-West Europe Campaign of 1944-1945 started with the landings in Normandy and ended with Field Marshal Montgomery taking the German military surrender of all German forces in Holland, Northwest Germany and Denmark on Lüneburg Heath in Northwest Germany was fought by the British 21st Army Group. In the First campaign the French Army was responsible for the rest of the Western Front from Luxembourg to Switzerland, as were the American 12th Army and 6th Army Groups during the second campaign.
Units of the First Canadian Army fought in five major campaigns in North-West Europe, including the Battle of Normandy, the battles for the Channel Ports, the Battle of the Scheldt, the Rhineland fighting in February and March 1945, and the final operations east of the River Rhine. A period of static warfare existed from 1 November 1944 to 8 February 1945 during which time the First Canadian Army manned positions in the Nijmegen Salient.