Sitzkrieg, or "Sitting War", is the British term for the time of relative military inactivity on continental Europe after Germany invaded Poland in World War II. It ended when Germany invaded France and the Low Countries in May 1940. 
The Saar Offensive
After declaring war, France sent eleven divisions across the German border. The French advanced aggressively, but were stalled at the Sigfried Line. After three days of bloody fighting, the French withdrew for good. The battle saw the first use of the "Stuka" bomber against the Allies.
Air War during the Sitzkrieg
Both the RAF and Luftwaffe were active during this time. However, British High Command was fearful of retaliation, so British bombing attacks were restricted to coastal or shipping targets. The ranges involved meant that the bombers were sent without fighter escort, relying instead on their defensive guns to protect them. These raids did some damage, but on two missions in December, the RAF lost 18 bombers (out of a total number of 36 sent). Bomber gunners shot down three fighters, but this marked the end of RAF daylight bombing attacks in Europe. RAF bombers ranged across Germany and reached as far as Berlin, Warsaw, and Prague, but these planes were armed not with bombs but propaganda leaflets.
German bombing was equally muted and confined to Royal Navy or shipping targets. British Fighter Command responded as the Luftwaffe did, and several bombers were lost.
As the Sitzkrieg wore on into the spring of 1940, German aerial activity along the French-German border intensified. This led to a number of engagements between British, French, and German fighters, which the Germans usually won. Future high-scoring aces Werner Molders and Adolf Galland both scored their first victories during this period.
Sea War during the Sitzkrieg
Most significant action during the Phony War was at sea. U-boats achieved some major successes. The aircraft carrier HMS Courageous was sunk by a submarine on September 12, and the carrier Ark Royal narrowly missed a similar fate 2 days later. The Kriegsmarine scored another victory in October when U-47 penetrated the Royal Navy base at Scapa Flow and sank the WWI-era battleship Royal Oak. However, U-boats were not yet available in sufficient numbers to be the threat they were later in the war.
The highlight of the sea war was the saga of the pocket battleship Graf Spee, which conducted a successful commerce raiding mission in the first months of the war, and fought with three British cruisers at the Battle of the River Platte in December 1939, damaging the Exeter so badly that she was later scrapped. The Graf Spee suffered less battle damage than her opponents, but she was forced to seek refuge in the port of Montevideo, where her crew scuttled her.
- “The Phoney War” October 1939 - April 1940
- Ju-87 Stukageschwader of the Western Front, by Jake Seal, Osprey Publishing, 1997
- Aircraft vs. Aircraft, by Norman Franks, Barnes & Noble Books, 1998
- Encyclopedia of Aircraft of WWII, ed. by Paul Eden, Aerospace Publishing, 2004
- Submarine Warfare, An Illustrated History, by Antony Preston, Thunder Bay Press, 1998