In World War II, Fall Gelb (Case Yellow in German) was the German invasion of France and the Low Countries, executed 10 May, 1940. German armored units punched through the Ardennes, outflanking the Maginot Line and unhinging the Allied defenders.
Fall Gelb had been elaborated by the famous General Erich von Manstein.
France fell in less than a month. Much of the British army and a large part of the Polish army was able to escape in a series of evacuations (Ariel, Dynamo). The French Republic collapsed and was replaced by an "État Français" ("French State" in French) headed by Marshal Henri Philippe Pétain. His government based in Vichy (hence the name, Vichy France) became a loyal partner of the Axis for the rest of the war. This campaign included Operation Rot.