By 6 October 1939, Poland had fallen and was divided between the Soviet Union and Germany. "The Phony War" followed, with the belligerents taking little--virtually no--action against each other.
One significant exception to this occurred two months later, when, on 13 December 1939, Royal Navy cruisers engaged the German pocket battleship Admiral Graf Spee off the Atlantic coast of South America and forced the damaged ship to seek refuge in Montevideo, Uruguay.
Diplomatic pressure (largely from the United States, although this was denied at the time) on Uruguay forced that small country to insist on following international law, which required belligerent vessels to leave sanctuary ports within seventy-two hours. On 17 December, Captain Hans Langsdorff, to save further loss of life in a battle he knew he could not win, scuttled the Graf Spee just outside the mouth of the Montevideo harbor. He then went to Argentina, buried his dead, made arrangements for the internment of his crew--and then shot himself in the temple, arranging that event so his body would fall on the German navy battle flag.
The Phony War turned real on the night of 9/10 May 1940, when the Germans occupied Luxembourg and launched another Blitzkrieg, this time into the Netherlands and Belgium. The Dutch surrendered 15 May.
On 5 June 1940, the Germans solved the problem of the "impregnable" French Maginot Line of fortresses by going around them. Paris fell on 14 June. Not all French were desolated; substantial numbers of them embraced the motto "Better Hitler Than Blum." Andre Leon Blum, a socialist, already had twice served as France's prime minister.
The French capitulated on 25 June 1940.
The only good news for the English during this period was their brilliant evacuation of 300,000 British soldiers and some 38,000 French from Dunkirk.
Germany began a massive aerial bombardment of England as the prelude to a cross-Channel invasion. The Royal Air Force's valiant and effective defense of Enland caused Winston Churchill, its prime minister, to utter the famous line "Never in the field of human conflict was so much owed by so many to so few."
The severe losses suffered by the Luftwaffe are cited by some historians as the reason Adolf Hitler called off the invasion. Other historians feel that it was Hitler's decision to stab the Soviet Union in the back that brought him to that decision. He would deal with the English after he had dealt with the Communists.