German invasion of Belgium (1940) in the context of Invasion of Luxembourg

The Battle of France (French: bataille de France; 10 May – 25 June 1940), also known as the Western Campaign (German: Westfeldzug), the French Campaign (Frankreichfeldzug, campagne de France) and the Fall of France, during the Second World War was the German invasion of the Low Countries (Belgium, Luxembourg and the Netherlands) and France. The plan for the invasion of the Low Countries and France was called Fall Gelb (Case Yellow or the Manstein plan). Fall Rot (Case Red) was planned to finish off the French and British after the evacuation at Dunkirk. The Low Countries and France were defeated and occupied by Axis troops down to the Demarcation line.

On 3 September 1939, France and Britain declared war on Nazi Germany, over the German invasion of Poland on 1 September. In early September 1939, the French army began the limited Saar Offensive but by mid-October had withdrawn to the start line. On 10 May 1940, Wehrmacht armies invaded Belgium, Luxembourg, the Netherlands and parts of France.

The military history of the United Kingdom in World War II covers the Second World War against the Axis powers, starting on 3 September 1939 with the declaration of war by the United Kingdom and France, followed by the UK's Dominions, Crown colonies and protectorates on Nazi Germany in response to the invasion of Poland by Germany. There was little, however, the Anglo-French alliance could do or did do to help Poland. The Phoney War culminated in April 1940 with the German invasion of Denmark and Norway. Winston Churchill became prime minister and head of a coalition government in May 1940. The defeat of other European countries followed – Belgium, the Netherlands, Luxembourg and France – alongside the British Expeditionary Force which led to the Dunkirk evacuation in June 1940.

Britain and its Empire continued the war against Germany. Churchill engaged industry, scientists and engineers to advise and support the government and the military in the prosecution of the war effort. Germany's planned invasion of the UK was averted by the Royal Air Force denying the Luftwaffe air superiority in the Battle of Britain, and by its marked inferiority in naval power. Subsequently, urban areas in Britain suffered heavy bombing during the Blitz in late 1940 and early 1941. The Royal Navy sought to blockade Germany and protect merchant ships in the Battle of the Atlantic. The Army counter-attacked in the Mediterranean and Middle East, including the North-African and East-African campaigns, and in the Balkans.

Army Group B (German: Heeresgruppe B) was the name of four distinct German army group commands that saw action during World War II.

The first Army Group B was created on 12 October 1939 (from the former Army Group North) and fought in the Battle of France on the northern flank. It was responsible for a part of the German invasion of Belgium and the majority of the German invasion of the Netherlands. In the later stage of that campaign ("Case Red"), it again advanced on the German right flank towards the Somme river, the city of Paris and the Franco-Spanish border. After 16 August 1940, it was deployed to East Prussia and to the General Government in German-occupied Poland. When Operation Barbarossa began on 22 June 1941, Army Group B was renamed on the same day to become "Army Group Center".

The Belgian Labour Party (Dutch: Belgische Werkliedenpartij, pronounced [ˈbɛlɣisə ˈʋɛrklidə(m)pɑrˌtɛi], BWP; French: Parti ouvrier belge, pronounced [paʁti uvʁije bɛlʒ], POB) was the first major socialist party in Belgium. Founded in 1885, the party achieved its first electoral breakthrough in the aftermath of World War I. It was officially disbanded after the German invasion of Belgium in 1940 and superseded by the Belgian Socialist Party in 1945.

World War II or the Second World War (1 September 1939 – 2 September 1945) was a global conflict between two coalitions: the Allies and the Axis powers. Nearly all of the world's countries participated, with many nations mobilising their resources in pursuit of total war. Tanks and aircraft played major roles, enabling the strategic bombing of cities and delivery of the first and only nuclear weapons ever used in war. World War II is the deadliest conflict in history, causing the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Germany, Austria, Japan, and Korea were occupied, and German and Japanese leaders were put on trial for war crimes.

The causes of World War II included unresolved tensions in the aftermath of World War I, the rise of fascism in Europe and militarism in Japan. Key events preceding the war included Japan's invasion of Manchuria in 1931, the Spanish Civil War, the outbreak of the Second Sino-Japanese War in 1937, and Germany's annexations of Austria and the Sudetenland. World War II is generally considered to have begun on 1 September 1939, when Nazi Germany, under Adolf Hitler, invaded Poland, after which the United Kingdom and France declared war on Germany. Poland was also invaded by the Soviet Union in mid-September, and was partitioned between Germany and the Soviet Union under the Molotov–Ribbentrop Pact. In 1940, the Soviet Union annexed the Baltic states and parts of Finland and Romania, while Germany conquered Norway, Belgium, Luxembourg and the Netherlands. After the fall of France in June 1940, the war continued mainly between Germany, now assisted by Fascist Italy, and the British Empire, with fighting in the Balkans, Mediterranean, and Middle East, East Africa, the aerial Battle of Britain and the Blitz, and the naval Battle of the Atlantic. By mid-1941 Yugoslavia and Greece had also been defeated by Axis countries. In June 1941, Germany invaded the Soviet Union, opening the Eastern Front and initially making large territorial gains along with Axis allies.